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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2013-08-20</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001196298</issuerCik>
        <issuerName>NEPHROS INC</issuerName>
        <issuerTradingSymbol>NEPH</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001179697</rptOwnerCik>
            <rptOwnerName>AMRON ARTHUR H</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O WEXFORD CAPITAL LP</rptOwnerStreet1>
            <rptOwnerStreet2>411 WEST PUTNAM AVENUE</rptOwnerStreet2>
            <rptOwnerCity>GREENWICH</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06830</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2013-08-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>5417</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>28763</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">On August 20, 2013, the Company granted 5,417 shares of restricted stock of the Company (the &quot;Restricted Stock&quot;) in respect of the service by Mr. Amron as a member of the Board of Directors of the Company.  The Restricted Stock was granted under the Company's 2004 Stock Incentive Plan.  At the request of Mr. Amron, the Restricted Stock was granted to Wexford Capital LP.  The Restricted Stock vests 6 months following the grant date.</footnote>
        <footnote id="F2">All grants of Restricted Stock, at the request of Mr. Amron, are granted to Wexford Capital LP.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Arthur H. Amron</signatureName>
        <signatureDate>2013-08-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
