U.S. forces said Monday they came under rocket attack hours after they carried out airstrikes against Iran-backed militia targets in Syria and Iraq in what officials had described as an effort to deter mounting violence by anti-American groups.

A spokesman for the U.S.-led coalition in Iraq and Syria, Col. Wayne Marotto, said that multiple rockets had targeted a facility housing U.S. troops near al-Omar oil field in northeast Syria. No casualties were reported. Marotto said U.S. forces responded in self-defense with artillery fire targeting positions where the rockets were launched.

No one claimed responsibility for the rocket attacks, but video of the assault was shared on Telegram social media channels used by the militias.

U.S. officials have said the American airstrikes carried out a night earlier were meant to stem militia attacks on U.S. forces, but the Iran-backed groups have sworn revenge, raising the prospect of a further escalation….