Three other service members were wounded, a military official said.
Until this week, just two American service members had been killed in Syria.
Allied aircraft bombed a mosque on Thursday that the Islamic State had used as a command center in Safafiyah, Syria, in the Middle Euphrates River Valley, the Pentagon said. It was unclear if the airstrike was in response to the attack in Manbij, scores of miles to the northwest, or, more likely, a target of opportunity.
Manbij was still in shock on Thursday, residents said, struggling to deal with the aftermath of the bombing and their town’s uncertain future should Mr. Trump make good on his promise to withdraw American troops. Turkey has talked about invading. The Syrian government and its Russian and Iranian allies want the territory back. And the Islamic State has proved it still has the ability to strike.
The attack added fuel to the debate over the ever-shifting American mission in eastern Syria, and President Trump’s plans to bring troops home.
While Mr. Trump and, as recently as Wednesday, Vice Mike President Pence, insisted that the Islamic State had been defeated, a range of American officials, including many of Mr. Trump’s allies, have said the attack proved otherwise and that leaving Syria could allow the jihadists to come roaring back.
Mr. Darwish, of the local military council, said that whether the United States ultimately withdraws or not, the existing confusion over American policy had emboldened the jihadists.
“ISIS benefits from the tense atmosphere, the murky situation, the recent statements, the decision to withdraw and the tweets from all over,” he said. “That has made the region unstable, and all of that helps ISIS to bring itself back together.”