BEIRUT—Islamic State said Tuesday it was behind the armed assault on an art fair in Texas where cartoons of the Prophet Muhammad were set to be exhibited, the first time the extremist group has claimed responsibility for an attack on U.S. soil.

In a broadcast by its official radio station in Iraq, Islamic State said two of its “soldiers” carried out Sunday’s attack in Garland, Texas. The claim couldn’t be independently confirmed, and a police spokesman in Garland declined to comment.

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