<?xml version="1.0"?>
<ownershipDocument>
    <schemaVersion>X0201</schemaVersion>

    <documentType>4</documentType>
<periodOfReport>2003-11-18</periodOfReport>
<notSubjectToSection16>0</notSubjectToSection16>
    <issuer>
        <issuerCik>0001093672</issuerCik>
        <issuerName>PEOPLES BANCORP OF NORTH CAROLINA INC</issuerName>
        <issuerTradingSymbol>PEBK</issuerTradingSymbol>
</issuer>
<reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001215311</rptOwnerCik>
            <rptOwnerName>ROBINSON LARRY E</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>518 WEST C STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEWTON</rptOwnerCity>
            <rptOwnerState>NC</rptOwnerState>
            <rptOwnerZipCode>28658</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
            <reportingOwnerRelationship>
<isDirector>1</isDirector>
<isOfficer>0</isOfficer>
<isTenPercentOwner>0</isTenPercentOwner>
<isOther>0</isOther>
<officerTitle></officerTitle>
<otherText></otherText>
</reportingOwnerRelationship>
</reportingOwner>
<nonDerivativeTable>
<nonDerivativeTransaction>
<securityTitle>
<value>Common Stock</value>
</securityTitle>
<transactionDate>
<value>2003-11-18</value>
</transactionDate>
<deemedExecutionDate>
</deemedExecutionDate>
<transactionCoding>
<transactionFormType>4</transactionFormType>
<transactionCode>J</transactionCode>
<equitySwapInvolved>0</equitySwapInvolved>
<footnoteId id="F1"/>
</transactionCoding>
<transactionTimeliness>
<value></value>
</transactionTimeliness>
<transactionAmounts>
<transactionShares>
<value>64.5946</value>
</transactionShares>
<transactionPricePerShare>
<value>18.30</value>
</transactionPricePerShare>
<transactionAcquiredDisposedCode>
<value>A</value>
</transactionAcquiredDisposedCode>
</transactionAmounts>
<postTransactionAmounts>
<sharesOwnedFollowingTransaction>
<value>19528.8728</value>
</sharesOwnedFollowingTransaction>
</postTransactionAmounts>
<ownershipNature>
<directOrIndirectOwnership>
<value>D</value>
</directOrIndirectOwnership>
<natureOfOwnership>
<value></value>
</natureOfOwnership>
</ownershipNature>
</nonDerivativeTransaction>
<nonDerivativeHolding>
<securityTitle>
<value>Common Stock</value>
</securityTitle>
<postTransactionAmounts>
<sharesOwnedFollowingTransaction>
<value>3177</value>
</sharesOwnedFollowingTransaction>
</postTransactionAmounts>
<ownershipNature>
<directOrIndirectOwnership>
<value>I</value>
</directOrIndirectOwnership>
<natureOfOwnership>
<value>By Wife</value>
</natureOfOwnership>
</ownershipNature>
</nonDerivativeHolding>
</nonDerivativeTable>
<footnotes>
<footnote id="F1">Directors and Officers Deferral Plan</footnote>
</footnotes>
<remarks></remarks>
<ownerSignature>
<signatureName>Larry E. Robinson</signatureName>
<signatureDate>2003-11-19</signatureDate>
</ownerSignature>
</ownershipDocument>

