U.S.-led troops backed by warplanes battled militants in southwestern Afghanistan, killing about a dozen rebels including several Taliban leaders, officials said Monday.

The U.S.-led coalition said its troops came under fire Sunday in the Khash Rod district of Nimroz province as they searched compounds for a Taliban leader suspected of involvement in suicide attacks.

The troops killed “multiple militant groups” with small-arms fire, and airstrikes killed two more groups of attackers, the coalition said. There were no coalition casualties, it said.

While the coalition said only that “several” militants died, Nimroz Gov. Ghulam Dastagir Azad said about a dozen rebels were killed. He said some of the bodies were torn apart in the late-night bombing.

Azad said the dead included three Taliban commanders, each of whom controlled a group of some 40-50 fighters. He said they were suspected of planning attacks on food relief convoys.

The U.N. reported Sunday that one of its relief convoys was attacked on its way to Nimroz and neighboring Helmand provinces, and that several trucks were burned. Other convoys have been looted.

More than 2,000 people have died in insurgency-related violence so far this year, according to an Associated Press tally based on reports by military and government officials.