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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-05-18</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000077543</issuerCik>
        <issuerName>TUTOR PERINI CORP</issuerName>
        <issuerTradingSymbol>TPC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001066062</rptOwnerCik>
            <rptOwnerName>KLEIN MICHAEL R</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O TUTOR PERINI CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>15901 OLDEN STREET</rptOwnerStreet2>
            <rptOwnerCity>SYLMAR</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>91342</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>2020-05-18</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>150000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>7.76</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>599890</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The price reported on Column 4 is a weighted average price. These shares were purchased in multiple transactions at prices ranging from $7.67 to $7.88, inclusive. The reporting person undertakes to provide to Tutor Perini Corporation, any security holder of Tutor Perini Corporation, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares purchased at each separate price within the range set forth in the footnote to this Form 4.</footnote>
    </footnotes>

    <remarks>Exhibit 24 - Power of Attorney</remarks>

    <ownerSignature>
        <signatureName>/s/ Anthony C. Fiore, Attorney-in-Fact</signatureName>
        <signatureDate>2020-05-20</signatureDate>
    </ownerSignature>
</ownershipDocument>
