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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2006-07-14</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000737207</issuerCik>
        <issuerName>NASTECH PHARMACEUTICAL CO INC</issuerName>
        <issuerTradingSymbol>NSTK</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001249004</rptOwnerCik>
            <rptOwnerName>YORK BRUCE R</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>3450 MONTE VILLA PKWY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>BOTHELL</rptOwnerCity>
            <rptOwnerState>WA</rptOwnerState>
            <rptOwnerZipCode>98021</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Chief Accounting Officer</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Nastech Pharmaceutical Company Inc Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2006-07-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3093</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>16842</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">On July 14, 2006 the reporting person was granted 3,093 restricted shares of common stock pursuant to the 2004 Stock Incentive Plan of Nastech Pharmaceutical Company Inc.  The restricted shares vest in three equal annual installments beginning on July 14, 2007.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Philip C. Ranker

Philip C. Ranker
Attorney in Fact</signatureName>
        <signatureDate>2006-07-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
