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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2010-02-23</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000319240</issuerCik>
        <issuerName>IRIS INTERNATIONAL INC</issuerName>
        <issuerTradingSymbol>IRIS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001343621</rptOwnerCik>
            <rptOwnerName>Yi John U</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O IRIS INTERNATIONAL, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>9172 ETON AVENUE</rptOwnerStreet2>
            <rptOwnerCity>CHATSWORTH</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>91311</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Corp VP, Operations</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>11.97</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2010-02-23</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>22684</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2017-02-23</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>22684</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>22684</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2010-02-23</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3342</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3342</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3342</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Vests 25% on February 23, 2011 and thereafter 6.25% will vest in 12 equal quarterly installments with the first such installment vesting on June 30, 2011.</footnote>
        <footnote id="F2">Each restricted stock unit represents a contingent right to receive one share of IRIS International, Inc. common stock.</footnote>
        <footnote id="F3">Vests 25% on March 23, 2011 and thereafter 6.25% will vest in 12 equal quarterly installments with the first such installment vesting on June 30, 2011.  Vested shares will be delivered to the reporting person as soon as practicable following the applicable vesting date.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Todd M. Graham, Attorney-In-Fact</signatureName>
        <signatureDate>2010-02-25</signatureDate>
    </ownerSignature>
</ownershipDocument>
