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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2006-05-26</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>2006-05-26</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>125000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>2.80</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1222652</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F1"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>I</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10914694</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>I</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>984615</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F4"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>I</value>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Securities directly owned by Chaumiere Consultadoria e Servicos S.A. (?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="F2">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="F3">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 40% of Sigma Tau.</footnote>
        <footnote id="F4">Securities directly owned by Sigma Tau.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Maurizio Terenzi, Attorney-in-fact</signatureName>
        <signatureDate>2006-05-30</signatureDate>
    </ownerSignature>
</ownershipDocument>
