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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-05-23</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001529922</rptOwnerCik>
            <rptOwnerName>Martell Robert</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>Head of Research &amp; Development</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee stock option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>1.16</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-05-23</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>386996</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2029-01-20</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>386996</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>386996</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">This option grant, as disclosed in Curis Inc.'s 2019 proxy statement, was approved by the Compensation Committee of the Board of Directors of Curis, Inc. on January 21, 2019, contingent upon shareholder approval of an amendment to Curis's Third Amended and Restated 2010 Stock Incentive Plan to increase the number of shares authorized for issuance thereunder; and further provided that such option would not be exercisable and no common stock would be issued thereunder, if the amendment to the Third Amended and Restated 2010 Plan was not approved by Curis's shareholders. On May 23, 2019, at the 2019 annual meeting of shareholders, Curis's shareholders approved the amendment to the Third Amended and Restated 2010 Plan. The option grant described in this Form 4 filing vests as to 25% of the original shares on January 21, 2020 and as to an additional 6.25% of the original shares each successive quarter and until January 21, 2023.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>William Steinkrauss,
Attorney-in-fact</signatureName>
        <signatureDate>2019-05-28</signatureDate>
    </ownerSignature>
</ownershipDocument>
