<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2004-01-02</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0001045609</issuerCik><issuerName>AMB PROPERTY CORP</issuerName>        <issuerTradingSymbol>AMB</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001213054</rptOwnerCik><rptOwnerName>FRIES DAVID S</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>C/O AMB PROPERTY CORPORATION</rptOwnerStreet1><rptOwnerStreet2>PIER 1, BAY 1</rptOwnerStreet2><rptOwnerCity>SAN FRANCISCO</rptOwnerCity><rptOwnerState>CA</rptOwnerState><rptOwnerZipCode>94111</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>0</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle>Executive VP</officerTitle></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeTransaction><securityTitle><value>Common Stock</value><footnoteId id="F1" /></securityTitle><transactionDate><value>2004-01-02</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>D</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>22357.0000</value></transactionShares><transactionPricePerShare><footnoteId id="F2" /></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>101413.0000</value><footnoteId id="F3" /></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeTransaction><securityTitle><value>Stock Units</value><footnoteId id="F1" /></securityTitle><transactionDate><value>2004-01-02</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>22357.0000</value></transactionShares><transactionPricePerShare><footnoteId id="F2" /></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>101413.0000</value><footnoteId id="F3" /></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>See footnote</value><footnoteId id="F4" /></natureOfOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><footnotes><footnote id="F1">Upon vesting of the 22,357 shares of restricted stock, the reporting person deferred these shares into the Amended and Restated AMB Nonqualified Deferred Compensation Plan (the "Plan").  The deferral of these shares was credited to the reporting person's account in the form of an equivalent number of stock units, each of which represents the reporting person's right to receive a share of AMB common stock upon distribution of his account.  Distribution will occur upon retirement, death, other termination of employment or disability, upon AMB's change of control or on such other date as the reporting person elects.</footnote><footnote id="F2">Solely a change in the form of ownership.</footnote><footnote id="F3">Of the 101,413 securities beneficially owned, 60,199 are directly owned (D) and 41,214 securities are held indirectly (I) through a rabbi trust pursuant to the Plan.</footnote><footnote id="F4">The stock units are held indirectly through a rabbi trust pursuant to the Plan.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ Tamra D. Browne pursuant to a power of attorney dated 01/15/2003.</signatureName><signatureDate>2004-01-05</signatureDate></ownerSignature></ownershipDocument>

