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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2005-11-20</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000310522</issuerCik>
        <issuerName>FEDERAL NATIONAL MORTGAGE ASSOCIATION FANNIE MAE</issuerName>
        <issuerTradingSymbol>FNM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001222983</rptOwnerCik>
            <rptOwnerName>NICULESCU PETER S</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>3900 WISCONSIN AVENUE, N.W.</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>WASHINGTON</rptOwnerCity>
            <rptOwnerState>DC</rptOwnerState>
            <rptOwnerZipCode>20016</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP, Mortgage Portfolio</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2005-11-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>322</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>47.9375</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>79902</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2005-11-21</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>322</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>48.535</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>79580</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>224.699</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By ESOP</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Under Fannie Mae's Performance Share Program, as a member of Fannie Mae's senior management, the reporting person has previously received awards that entitle the reporting person to receive shares of Fannie Mae common stock in an amount based upon and subject to Fannie Mae's  meeting corporate performance objectives over three-year periods.  These objectives are based on both financial and non-financial goals, equally weighted.  The financial goals under the performance share program are currently tied to growth in core business earnings per share.  Generally, Fannie Mae's Compensation Committee determines in January of the year following completion of the cycle the number of shares of common stock each awardee is entitled to receive, and the shares are paid out in two annual installments that January.  (Footnote 1 is continued in 2 below.)</footnote>
        <footnote id="F2">For the three-year performance cycle completed in 2003, the reporting person was determined in January 2004 to be entitled to receive 8,595 shares, of which the reporting person was paid 4,297 shares in accordance with the program and the remaining shares were expected to be paid in January 2005.  As previously announced, Fannie Mae will restate its previously issued financial statements and re-evaluate previously issued non-GAAP financial information, including core business earnings. The Compensation Committee and the Board of Directors of Fannie Mae have determined to consider the impact of Fannie Mae's restatement and re-evaluation on unpaid performance shares for the performance cycle completed in 2003 when reliable financial data for the relevant period are available.  As a result, 4,298 shares expected to be issued to the reporting person in January 2005 have not yet been issued.  These shares are included in the reporting person's total holdings above.</footnote>
        <footnote id="F3">End of period holdings include additional shares acquired from the reinvestment of dividends in Issuer's ESOP through August 25, 2005.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Peter S. Niculescu</signatureName>
        <signatureDate>2005-11-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
