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

    <schemaVersion>X0305</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-03-29</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001419806</issuerCik>
        <issuerName>RARE ELEMENT RESOURCES LTD</issuerName>
        <issuerTradingSymbol>REE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001343721</rptOwnerCik>
            <rptOwnerName>Ranta Donald E</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>225 UNION BLVD.</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 250</rptOwnerStreet2>
            <rptOwnerCity>LAKEWOOD</rptOwnerCity>
            <rptOwnerState>CO</rptOwnerState>
            <rptOwnerZipCode>80228</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>15.16</value>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2012-03-29</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>100000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2011-01-11</value>
            </exerciseDate>
            <expirationDate>
                <value>2016-01-11</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>100000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The exercise price is reflected in Canadian dollars.</footnote>
        <footnote id="F2">The reporting person and the Company agreed to cancellation of this option for no value and the Board of Directors approved such cancellation on March 29, 2012.  While no Section 16 report is required for this transaction, the reporting person has elected to file this Form 4 to be consistent with his Canadian insider reports.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Donald E. Ranta</signatureName>
        <signatureDate>2012-04-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
