WASHINGTON—President Barack Obama is close to authorizing a mission led by the U.S. military to train moderate Syrian rebels to fight the regime and al Qaeda-linked groups, a move that would significantly expand Washington's role in the conflict, U.S. officials said.

A new military training program, if implemented, would supplement a small train-and-equip program led by the Central Intelligence Agency that Mr. Obama authorized a year ago. U.S. officials don't discuss the CIA's limited training program because it is covert.

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