Kabul, Afghanista ? Fighting raged across southern Afghanistan on Sunday as the U.S. military pounded suspected Taliban positions with airstrikes that killed as many as 20 militants along a narrow mountain footpath.

A Taliban spokesman, meanwhile, claimed his fighters had assassinated a kidnapped Afghan police chief and five of his men for collaborating with the U.S.-led coalition.

U.S. aircraft opened fire on a group of suspected Taliban along a narrow footpath in the high mountains northwest of Gereshk, in southern Helmand province, after rebels had pinned down a coalition ground patrol with rocket and small-arms fire.

“Initial battle-damage assessments indicate 15 to 20 enemies died and an enemy vehicle was destroyed,” the army said in a statement. No Americans were injured.

A U.S soldier watches the landing of a U.S. Chinook helicopter Sunday at an airfield in Laghman province, east of Kabul, Afghanistan.

Military spokesman Lt. Col. Jerry O’Hara added a warning to the insurgents.

“When these criminals engage coalition forces, they do so at considerable risk,” he said. “We are not going to let up on them. There is not going to be a safe haven in Afghanistan.”

O’Hara told The Associated Press that additional U.S. and Afghan forces had been sent to the scene and the numbers of rebel dead could rise.

Three months of bloodshed across the south and east has left hundreds dead and sparked fears that the Afghan war is widening, rather than winding down.

Afghan and American officials have warned they expect more bloodshed ahead of key parliamentary elections in September.

Some 260 suspected rebels and 29 U.S. troops have been killed since March, according to Afghan and U.S. officials. About three dozen Afghan police and soldiers also have died, as have more than 100 civilians.