Nearly a week after a U.S. missile strike killed or wounded six Pakistani soldiers, the United States apologized Wednesday, acknowledging that two of its Afghanistan-based assault helicopters had entered Pakistani airspace “several times” and mistakenly fired at a military post.

Statements from the U.S. Embassy in Islamabad and coalition force headquarters in Kabul largely agreed with Pakistan’s initial assessment that its troops had fired rifle shots to warn the helicopters they were on the Pakistani side of the border. The helicopters, on an anti-insurgent mission, responded with missiles that destroyed the post, killing two Pakistanis and wounding four. Coalition statements initially said the missiles were fired in self-defense.

“We deeply regret this tragic loss of life and will continue to work with the Pakistan military and government to ensure this doesn’t happen again,” Gen. David Petraeus, the coalition commander in Afghanistan, said in a military statement that pledged better coordination. U.S. Ambassador Anne Patterson extended “our deepest apology to Pakistan and the families” of the casualties.

A senior Pakistani military official described the statements as “good gestures” that would be “taken positively by everybody in Pakistan,” along with an assurance that “these attacks won’t be repeated.” Pakistan had demanded a statement of fault and an apology.