WASHINGTON—The U.S. is poised to concede for the first time that it bears significant responsibility for last month's American airstrike that killed 24 Pakistani troops, U.S. officials said, an admission that is expected to embarrass the American military but points to a way out of the deepening mistrust between the two countries.

A military investigation has found that U.S. and Afghan commandos incorrectly concluded there were no Pakistani forces in the Afghan border area where the coalition was conducting an operation on...