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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2008-12-10</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000707511</issuerCik>
        <issuerName>REGENERX BIOPHARMACEUTICALS INC</issuerName>
        <issuerTradingSymbol>RGN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001163608</rptOwnerCik>
            <rptOwnerName>CAVAZZA PAOLO</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>VIA TESSERETE 10</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>LUGANO</rptOwnerCity>
            <rptOwnerState>V8</rptOwnerState>
            <rptOwnerZipCode>00000</rptOwnerZipCode>
            <rptOwnerStateDescription>SWITZERLAND</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2008-12-10</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1034482</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1.45</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5590467</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Indirect</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12011185</value>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F5"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Indirect</value>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>984615</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F6"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Indirect</value>
                    <footnoteId id="F6"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Common Stock Warrant (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>1.74</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2008-12-10</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F7"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2008-12-10</value>
            </exerciseDate>
            <expirationDate>
                <value>2011-12-31</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>372552</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Indirect</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">These 1,034,482 shares (the ?Shares?) were acquired on December 10, 2008 pursuant to a purchase agreement with the Issuer that provides that the Issuer, rather than Chaumiere Consultadoria e Servicos SDC Unipessoal L.d.a. (?Chaumiere?), has all voting rights in respect of the Shares through December 31, 2011, and that Chaumiere may not transfer the Shares through December 31, 2011 except for transfers to Affiliates (as defined therein).</footnote>
        <footnote id="F2">2,500,000 of these shares were acquired on February 29, 2008 pursuant to a purchase agreement with the Issuer that provides that the Issuer shall have the right to repurchase the shares at any time until December 31, 2009, for $2.00 per share, or at any time between January 1, 2010 and December 31, 2010, for $2.50 per share.  Furthermore, the purchase agreement provides that the Issuer, rather than Chaumiere, has all voting rights in respect to the shares through December 31, 2010, and that Chaumiere may not transfer the shares through December 31, 2010 except for transfers to Affiliates (as defined therein).</footnote>
        <footnote id="F3">Securities directly owned by Chaumiere, which is an indirect wholly-owned subsidiary of Aptafin S.p.A. (?Aptafin?). Aptafin is owned by Paolo Cavazza and members of his family.</footnote>
        <footnote id="F4">307,692 of these shares were acquired on June 22, 2005 pursuant to a purchase agreement with the Issuer that provides that Defiante (as defined below) may not dispose of the shares for a five-year period (the ?Holding Period?), that the Issuer, rather than Defiante, has all voting rights in respect of the shares during the Holding Period, and that the Issuer shall have the right to repurchase the shares within 30 days of the expiration of the Holding Period at a price of $5.00 per share, provided that the Issuer may only repurchase an amount of shares that would leave Defiante, when combined with all of its affiliates, with no less than 30.1% of the Issuer?s shares of Common Stock.</footnote>
        <footnote id="F5">Securities directly owned by Defiante Farmaceutica L.D.A. (?Defiante?). Defiante is 58% directly owned by Sigma Tau Finanziaria S.p.A. (?Sigma Tau?) and 42% directly owned by Sigma Tau?s wholly-owned subsidiary, Sigma Tau International S.A. Paolo Cavazza directly and indirectly owns 38% of Sigma Tau.</footnote>
        <footnote id="F6">Securities directly owned by Sigma Tau.</footnote>
        <footnote id="F7">This warrant was issued by the Issuer to Chaumiere in consideration of Chaumiere?s purchase of the Shares.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Fabio Poma, Attorney-in-fact</signatureName>
        <signatureDate>2008-12-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
