WASHINGTON  A military investigation has concluded that American personnel made significant errors in carrying out some of the airstrikes in western Afghanistan on May 4 that killed dozens of Afghan civilians, according to a senior American military official.

The official said the civilian death toll would probably have been reduced if American air crews and forces on the ground had followed strict rules devised to prevent civilian casualties. Had the rules been followed, at least some of the strikes by American warplanes against half a dozen targets over seven hours would have been aborted.

The report represents the clearest American acknowledgment of fault in connection with the attacks. It will give new ammunition to critics, including many Afghans, who complain that American forces too often act indiscriminately in calling in airstrikes, jeopardizing the United States mission by turning the civilian population against American forces and their ally, the Afghan government.

Since the raid, American military commanders have promised to address the problem. On Tuesday, Lt. Gen. Stanley A. McChrystal, nominated to be the American commander in Afghanistan, vowed that reducing civilian casualties was “essential to our credibility.”