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.

The Pentagon said it conducted a series of airstrikes in and around the Syrian town of Ma’ra on May 27 and May 28. The Pentagon-backed Mutasim Brigade said one of the airstrikes hit the brigade.

A statement issued by the U.S. military at the time said three strikes were carried out near Ma’ra that “struck two separate ISIL tactical units and destroyed two ISIL tactical vehicles and an ISIL vehicle,” using the Pentagon’s preferred acronym for Islamic State.

But leaders with the brigade in interviews said a U.S. airstrike hit brigade members while they were fighting Islamic State militants. Mustafa Sejry, the head of Mutasim’s political office, said 10 of the brigade’s fighters were killed in the U.S. strike.

A spokesman for the U.S. military’s Central Command acknowledged the incident, saying in a written statement that the U.S. military had launched an investigation.

“Initial reports were that four counter-ISIL personnel may have been killed in the strike,” said Col. Patrick Ryder, who is based in Tampa, Fla. It wasn’t immediately clear why there was a discrepancy in casualty figures.

“An investigation into this incident has been initiated. We will continue our support to counter-ISIL forces and will apply any lessons learned derived from the investigation to improve our operations in the future,” Col. Ryder added.

The errant airstrike is the first apparent friendly-fire event acknowledged by U.S. Central Command involving U.S. forces in Syria. The only other such incident in the fight against Islamic State happened in Iraq and was publicly disclosed by Central Command in December 2015.

It is unclear why the U.S. military didn’t disclose the Syria incident earlier. Col. Ryder said that the “dynamic and complex nature of the battlefield” contributes to a lag time in reporting from local forces on the ground.

“In this case, several days transpired before coalition forces were made aware of the potential friendly fire incident,” Col. Ryder said.

The incident comes as the U.S. military has stepped up efforts to help local forces in northern Syria clear Islamic State from a crucial stretch near the border with Turkey.

Mr. Sejry said the U.S. airstrike hit Pentagon-backed forces when they were 400 meters from Islamic State positions during an intense period of fighting near Ma’ra.

After the strike, a representative of the U.S. military told Mr. Sejry that U.S. aircraft accidentally hit the brigade’s fighters and offered an apology, according to Mr. Sejry.

“They apologized and stated that it was by mistake,” Mr. Sejry said. “And we have no other choice than to say maybe it was mistake.”

Members of the brigade were vetted by the U.S. military before receiving weaponry and equipment under the program, according to Mr. Sejry.

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