<?xml version="1.0"?><ownershipDocument>
    <schemaVersion>X0201</schemaVersion>

    <documentType>4</documentType><periodOfReport>2003-10-21</periodOfReport><notSubjectToSection16>0</notSubjectToSection16>
    <issuer>
        <issuerCik>0000310522</issuerCik>
        <issuerName>FEDERAL NATIONAL MORTGAGE ASSOCIATION FANNIE MAE</issuerName>
        <issuerTradingSymbol>FNM</issuerTradingSymbol></issuer><reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001026921</rptOwnerCik>
            <rptOwnerName>MARRON DONALD B</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O FANNIE MAE,</rptOwnerStreet1>
            <rptOwnerStreet2>3900 WISCONSIN AVENUE, NW</rptOwnerStreet2>
            <rptOwnerCity>WASHINGTON</rptOwnerCity>
            <rptOwnerState>DC</rptOwnerState>
            <rptOwnerZipCode>20016</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
            <reportingOwnerRelationship>
<isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeTransaction><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-10-21</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>2600</value><footnoteId id="F1" /></transactionShares><transactionPricePerShare><value>0</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>4471</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><footnotes><footnote id="F1">New restricted stock award which vests at a rate of 25 percent per year on the day before each annual meeting of Fannie Mae shareholders beginning in 2004.  </footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ Iris Aberbach, Attorney-in-Fact
for Donald B. Marron</signatureName><signatureDate>2003-10-21</signatureDate></ownerSignature></ownershipDocument>

