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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-05-27</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001108205</issuerCik>
        <issuerName>CURIS INC</issuerName>
        <issuerTradingSymbol>CRIS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001271411</rptOwnerCik>
            <rptOwnerName>GRAY MICHAEL</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>4 MAGUIRE ROAD</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>LEXINGTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02421</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>CFO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee stock option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>2.39</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-05-27</value>
                <footnoteId id="F1"/>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>80000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2025-02-09</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>80000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>80000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">This option grant was approved by the Compensation Committee of the Board of Directors of Curis, Inc. on February 9, 2015, provided that such option would terminate and be forfeited if Curis' stockholders did not approve an amendment to Curis' Amended and Restated 2010 Stock Incentive Plan to increase the number of shares authorized for issuance thereunder within 12 months of the grant date; and further provided that such option would not be exercisable and no common stock would be issued thereunder, before the approval of such Stock Incentive Plan Amendment by Curis' stockholders.  On May 27, 2015, at its 2015 annual meeting of stockholders, the Curis' stockholders approved the Stock Incentive Plan Amendment.  The option vests and becomes exercisable as to 25% of the shares underlying the option on February 9, 2016, and as to an additional 6.25% of the shares underlying the option at the end of each subsequent quarter thereafter, based upon Mr. Gray's continued employment.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Michael P. Gray</signatureName>
        <signatureDate>2015-05-28</signatureDate>
    </ownerSignature>
</ownershipDocument>
