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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2017-08-11</periodOfReport>

    <dateOfOriginalSubmission>2017-08-15</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001202806</issuerCik>
        <issuerName>FEDERATED PREMIER INTERMEDIATE MUNICIPAL INCOME FUND</issuerName>
        <issuerTradingSymbol>FPT</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001061438</rptOwnerCik>
            <rptOwnerName>DONAHUE THOMAS R</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>FEDERATED INVESTORS TOWER</rptOwnerStreet1>
            <rptOwnerStreet2>1001 LIBERTY AVENUE</rptOwnerStreet2>
            <rptOwnerCity>PITTSBURGH</rptOwnerCity>
            <rptOwnerState>PA</rptOwnerState>
            <rptOwnerZipCode>15222-3779</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>Trustee &amp; Treas. of FIMCO</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2017-08-11</value>
                <footnoteId id="F1"/>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness></transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1825</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>14.13</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1525</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">This Form 4 amendment is filed to report the number of common shares accepted by and sold to the Issuer in the Issuer's tender offer. Due to oversubscription of the tender offer, the Issuer accepted properly tendered common shares on a pro rata basis. All common shares tendered by the reporting person that were not accepted have been returned. The final proration factor for the tender offer is .545064378.</footnote>
        <footnote id="F2">The sales price of $14.13 per common share represents 98 percent of the net asset value per common share determined as of the close of the regular trading session of the New York Stock Exchange on August 11, 2017, which is the expiration date for the tender offer.</footnote>
    </footnotes>

    <remarks>The previously filed power of Attorney dated May 14, 2015 is incorporated by reference.</remarks>

    <ownerSignature>
        <signatureName>/s/Thomas R. Donahue by his attorney-in-fact George F. Magera</signatureName>
        <signatureDate>2017-08-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
