WASHINGTON—The U.S. military bombed a Syrian rebel unit it had trained and equipped in a friendly-fire incident in late May, prompting an internal investigation and raising questions about renewed Pentagon efforts to build local forces to battle Islamic State.

The military didn’t disclose the incident until asked about it by The Wall Street Journal. It is the most serious setback to date for the Pentagon’s recent efforts to work with Sunni Arab forces in northern Syria.

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