<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-05-05</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000867665</issuerCik>
        <issuerName>ABRAXAS PETROLEUM CORP</issuerName>
        <issuerTradingSymbol>AXAS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001070032</rptOwnerCik>
            <rptOwnerName>POWELL PAUL A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>18803 MEISNER DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SAN ANTONIO</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>78258</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Director Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>3.66</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-05-05</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>25000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>3.66</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2015-05-05</value>
            </exerciseDate>
            <expirationDate>
                <value>2025-05-05</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Abraxas Petroleum Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>25000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>25000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeHolding>
            <securityTitle>
                <value>Director Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>5.38</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2014-05-06</value>
            </exerciseDate>
            <expirationDate>
                <value>2024-05-06</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Abraxas Petroleum Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>12000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Director Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>2.39</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2013-05-14</value>
            </exerciseDate>
            <expirationDate>
                <value>2023-05-14</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Abraxas Petroleum Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>12000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Director Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>2.90</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2012-05-04</value>
            </exerciseDate>
            <expirationDate>
                <value>2022-05-04</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Abraxas Petroleum Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>12000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Director Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>4.13</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2011-05-05</value>
            </exerciseDate>
            <expirationDate>
                <value>2021-05-05</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Abraxas Petroleum Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10500</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10500</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Director Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>2.36</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2010-05-19</value>
            </exerciseDate>
            <expirationDate>
                <value>2020-05-19</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Abraxas Petroleum Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Director Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>1.06</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2009-05-21</value>
            </exerciseDate>
            <expirationDate>
                <value>2019-05-21</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Abraxas Petroleum Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Director Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.99</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2009-03-17</value>
            </exerciseDate>
            <expirationDate>
                <value>2019-03-17</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Abraxas Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>50000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>50000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Director Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>4.32</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2007-06-26</value>
            </exerciseDate>
            <expirationDate>
                <value>2017-06-26</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Abraxas Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Director Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>4.59</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2005-09-13</value>
            </exerciseDate>
            <expirationDate>
                <value>2015-09-13</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Abraxas Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>45000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>45000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Director Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>4.51</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2006-05-25</value>
            </exerciseDate>
            <expirationDate>
                <value>2016-05-25</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Abraxas Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Director Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>4.50</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2008-05-21</value>
            </exerciseDate>
            <expirationDate>
                <value>2018-05-21</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Abraxas Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Director Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>2.75</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2005-06-01</value>
            </exerciseDate>
            <expirationDate>
                <value>2015-06-01</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Abraxas Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes></footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>PAUL A POWELL, JR.</signatureName>
        <signatureDate>2015-05-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
