WASHINGTON—Pakistani officials at a border coordination center gave the go-ahead to American airstrikes that inadvertently killed 24 Pakistan troops, unaware that their own forces were in the area, according to U.S. officials briefed on the preliminary investigation.

U.S. officials, giving their first detailed explanation of the worst friendly-fire incident of the 10-year-old war in Afghanistan, said an Afghan-led assault force that included American commandos were hunting Taliban militants when they...