NEW DELHI — Faced with outrage from a key ally, the American military yesterday released footage of a clash between coalition forces and Taliban militants that Pakistan alleges killed 11 of its soldiers.

The unusual move by military officials was clearly designed to soothe anger in Pakistan and to bolster their account of what happened in the rugged Afghan-Pakistani border region on Tuesday, when American warplanes dropped bombs during a pitched battle with militants.

The Pakistani army says the airstrike was an “unprovoked and cowardly act” that killed its paramilitary soldiers, while the American military insists that its forces acted within accepted rules of engagement and launched the strike in self-defense.

The incident has put a strain on already fragile relations between Washington and the newly elected Pakistani government. The Bush administration has long counted Pakistan as a front-line ally in the battle against Islamic extremism, but the new government in Islamabad has opted to negotiate with militants and resents what it sees as American disregard for its sovereignty.

Pakistani military officials say that the clash between American-led allied troops and militants just inside Afghanistan on Tuesday night culminated in a deadly airstrike on the Pakistani border outpost at Goraprai, in which a major and 10 other members of the Mohmand Rifles paramilitary force were killed.

But the U.S. military asserts that the footage released yesterday, shot by an unmanned aerial drone, absolves American forces of responsibility for those deaths.

The gray, grainy 6 1/2-minute video appears to show militants gathered on a hilltop in Afghanistan’s mountainous Kunar province, a vantage point from which they rain down small-arms and rocket fire on coalition troops below. A voice-over explains that the coalition soldiers then try to regroup at a location where a helicopter crew could rescue them.