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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2014-09-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000874238</issuerCik>
        <issuerName>STERLING CONSTRUCTION CO INC</issuerName>
        <issuerTradingSymbol>STRL</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001612339</rptOwnerCik>
            <rptOwnerName>HOLLAND PETER J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1800 HUGHES LANDING BLVD.</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 250</rptOwnerStreet2>
            <rptOwnerCity>THE WOODLANDS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>77380</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Senior Vice President</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2014-09-17</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>728</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>7.70</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8561</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">These shares were part of a restricted stock award, a portion of which was released from restrictions on September 16, 2013.  The shares were retained by the Company at the request of the Reporting Person pursuant to a procedure approved by the Compensation Committee of the Board of Directors to satisfy the Company's tax withholding requirements (based on the closing price of the Company's common stock on the release date) arising from the release of restrictions as permitted by the plan pursuant to which the restricted stock award was made.</footnote>
        <footnote id="F2">Of these shares 6,626 shares are subject to restrictions on their sale or other transfer and to forfeiture under certain circumstances.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Roger M. Barzun under a Power of Attorney</signatureName>
        <signatureDate>2014-09-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
