In an audio statement on Tuesday on the Islamic State's Al Bayan radio station, the extremist group claimed responsibility for the attack outside a Texas exhibit of caricatures of the Prophet Muhammad, 6ABC reports.
The statement said that "two soldiers of the caliphate" were responsible for Sunday's attack.
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The IS statement says: "We tell America that what is coming is more bitter and harder and you will see from the soldiers of the Caliphate what harms you."
The two gunmen who opened fire on Sunday at the exhibit near Dallas were shot dead at the scene.
Two law enforcement officials who asked not to be named identified one of the dead shooters as Elton Simpson, under surveillance since 2006 and convicted in 2010 of lying to FBI agents over his desire to join violent jihad in Somalia. The second shooter was identified as Nadir Soofi, a roommate of Simpson, according to two sources close to the investigation.
The event in Garland, Texas, organized by the American Freedom Defense Initiative (AFDI), was called "Muhammad Art Exhibit and Contest" and offered a $10,000 prize for the best artwork or cartoon depicting the prophet.
Reuters contributed to this report.