<?xml version="1.0"?>
<ownershipDocument>
    <schemaVersion>X0101</schemaVersion>

    <documentType>4</documentType>
<periodOfReport>2003-06-03</periodOfReport>
<notSubjectToSection16>0</notSubjectToSection16>
    <issuer>
        <issuerCik>0000831959</issuerCik>
        <issuerName>UNITED NATIONAL BANCORP</issuerName>
        <issuerTradingSymbol>UNBJ</issuerTradingSymbol>
</issuer>
<reportingOwner>
<reportingOwnerId>
            <rptOwnerCik>0001209430</rptOwnerCik>
            <rptOwnerName>WALKER DAVID R</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>  </rptOwnerStreet1>
            <rptOwnerStreet2>  </rptOwnerStreet2>
            <rptOwnerCity>  </rptOwnerCity>
            <rptOwnerState>  </rptOwnerState>
            <rptOwnerZipCode>  </rptOwnerZipCode>
        </reportingOwnerAddress>
            <reportingOwnerRelationship>
<isDirector>1</isDirector>
<isOfficer>0</isOfficer>
<isTenPercentOwner>0</isTenPercentOwner>
<isOther>0</isOther>
</reportingOwnerRelationship>
</reportingOwner>
<nonDerivativeSecurity>
<securityTitle>
<value>Common Stock</value>
</securityTitle>
<transactionDate>
<value>2003-06-03</value>
</transactionDate>
<deemedExecutionDate>
<value>2003-06-03</value>
</deemedExecutionDate>
<transactionCoding>
<transactionFormType>4</transactionFormType>
<transactionCode>G</transactionCode>
<equitySwapInvolved>0</equitySwapInvolved></transactionCoding>
<transactionAmounts>
<transactionShares>
<value>2000</value>
</transactionShares>
<transactionValue>
<value>0</value>
</transactionValue>
<transactionAcquiredDisposedCode>
<value>D</value>
<footnoteId id="F1"/>
</transactionAcquiredDisposedCode>
</transactionAmounts>
<postTransactionAmounts>
<sharesOwnedFollowingTransaction>
<value>37055</value>
</sharesOwnedFollowingTransaction>
</postTransactionAmounts>
<ownershipNature>
<directOrIndirectOwnership>
<value>D</value>
</directOrIndirectOwnership>
</ownershipNature>
</nonDerivativeSecurity>
<nonDerivativeSecurity>
<securityTitle>
<value>Common Stock</value>
</securityTitle>
<transactionDate>
<value>2003-06-03</value>
</transactionDate>
<deemedExecutionDate>
<value>2003-06-03</value>
</deemedExecutionDate>
<transactionCoding>
<transactionFormType>4</transactionFormType>
<transactionCode>G</transactionCode>
<equitySwapInvolved>0</equitySwapInvolved></transactionCoding>
<transactionAmounts>
<transactionShares>
<value>400</value>
</transactionShares>
<transactionValue>
<value>0</value>
</transactionValue>
<transactionAcquiredDisposedCode>
<value>D</value>
<footnoteId id="F2"/>
</transactionAcquiredDisposedCode>
</transactionAmounts>
<postTransactionAmounts>
<sharesOwnedFollowingTransaction>
<value>36655</value>
</sharesOwnedFollowingTransaction>
</postTransactionAmounts>
<ownershipNature>
<directOrIndirectOwnership>
<value>D</value>
</directOrIndirectOwnership>
</ownershipNature>
</nonDerivativeSecurity>
<nonDerivativeSecurity>
<securityTitle>
<value>Common Stock</value>
</securityTitle>
<transactionDate>
<value>2003-06-03</value>
</transactionDate>
<deemedExecutionDate>
<value>2003-06-03</value>
</deemedExecutionDate>
<transactionCoding>
<transactionFormType>4</transactionFormType>
<transactionCode>G</transactionCode>
<equitySwapInvolved>0</equitySwapInvolved></transactionCoding>
<transactionAmounts>
<transactionShares>
<value>400</value>
</transactionShares>
<transactionValue>
<value>0</value>
</transactionValue>
<transactionAcquiredDisposedCode>
<value>D</value>
<footnoteId id="F3"/>
</transactionAcquiredDisposedCode>
</transactionAmounts>
<postTransactionAmounts>
<sharesOwnedFollowingTransaction>
<value>36255</value>
</sharesOwnedFollowingTransaction>
</postTransactionAmounts>
<ownershipNature>
<directOrIndirectOwnership>
<value>D</value>
</directOrIndirectOwnership>
</ownershipNature>
</nonDerivativeSecurity>
<nonDerivativeSecurity>
<securityTitle>
<value>Common Stock</value>
</securityTitle>
<transactionDate>
<value>2003-06-03</value>
</transactionDate>
<deemedExecutionDate>
<value>2003-06-03</value>
</deemedExecutionDate>
<transactionCoding>
<transactionFormType>4</transactionFormType>
<transactionCode>G</transactionCode>
<equitySwapInvolved>0</equitySwapInvolved></transactionCoding>
<transactionAmounts>
<transactionShares>
<value>2000</value>
</transactionShares>
<transactionValue>
<value>0</value>
</transactionValue>
<transactionAcquiredDisposedCode>
<value>A</value>
<footnoteId id="F4"/>
</transactionAcquiredDisposedCode>
</transactionAmounts>
<postTransactionAmounts>
<sharesOwnedFollowingTransaction>
<value>38255</value>
</sharesOwnedFollowingTransaction>
</postTransactionAmounts>
<ownershipNature>
<directOrIndirectOwnership>
<value>I</value>
</directOrIndirectOwnership>
<natureOfOwnership>
<value>wife</value>
</natureOfOwnership>
</ownershipNature>
</nonDerivativeSecurity>
<nonDerivativeSecurity>
<securityTitle>
<value>Common Stock</value>
</securityTitle>
<transactionDate>
<value>2003-06-03</value>
</transactionDate>
<deemedExecutionDate>
<value>2003-06-03</value>
</deemedExecutionDate>
<transactionCoding>
<transactionFormType>4</transactionFormType>
<transactionCode>G</transactionCode>
<equitySwapInvolved>0</equitySwapInvolved></transactionCoding>
<transactionAmounts>
<transactionShares>
<value>600</value>
</transactionShares>
<transactionValue>
<value>0</value>
</transactionValue>
<transactionAcquiredDisposedCode>
<value>D</value>
<footnoteId id="F5"/>
</transactionAcquiredDisposedCode>
</transactionAmounts>
<postTransactionAmounts>
<sharesOwnedFollowingTransaction>
<value>37655</value>
</sharesOwnedFollowingTransaction>
</postTransactionAmounts>
<ownershipNature>
<directOrIndirectOwnership>
<value>I</value>
</directOrIndirectOwnership>
<natureOfOwnership>
<value>wife</value>
</natureOfOwnership>
</ownershipNature>
</nonDerivativeSecurity>
<nonDerivativeSecurity>
<securityTitle>
<value>Common Stock</value>
</securityTitle>
<transactionDate>
<value>2003-06-03</value>
</transactionDate>
<deemedExecutionDate>
<value>2003-06-03</value>
</deemedExecutionDate>
<transactionCoding>
<transactionFormType>4</transactionFormType>
<transactionCode>G</transactionCode>
<equitySwapInvolved>0</equitySwapInvolved></transactionCoding>
<transactionAmounts>
<transactionShares>
<value>600</value>
</transactionShares>
<transactionValue>
<value>0</value>
</transactionValue>
<transactionAcquiredDisposedCode>
<value>D</value>
<footnoteId id="F6"/>
</transactionAcquiredDisposedCode>
</transactionAmounts>
<postTransactionAmounts>
<sharesOwnedFollowingTransaction>
<value>37055</value>
</sharesOwnedFollowingTransaction>
</postTransactionAmounts>
<ownershipNature>
<directOrIndirectOwnership>
<value>I</value>
</directOrIndirectOwnership>
<natureOfOwnership>
<value>wife</value>
</natureOfOwnership>
</ownershipNature>
</nonDerivativeSecurity>
<footnotes>
<footnote id="F1">Gifted 2,000 shares to Mr. Walker's spouse.</footnote>
<footnote id="F2">Gifted 400 shares to Leigh Anderson (child)</footnote>
<footnote id="F3">Gifted 400 shares to Jane Summers (child).</footnote>
<footnote id="F4">Received as gift 2000 shares from spouse, Mr. Walker.</footnote>
<footnote id="F5">Gifted 600 shares to Leigh Anderson (child) from Mrs. Walker</footnote>
<footnote id="F6">Gifted 600 shares to Jayne Summers (child) from Mrs. Walker</footnote>
</footnotes>
<ownerSignature>
<signatureName>David R. Walker</signatureName>
<signatureDate>2003-06-04</signatureDate>
</ownerSignature>
</ownershipDocument>

