KABUL—U.S. and Afghan authorities investigated Saturday whether a botched NATO airstrike was to blame for the death of Afghan soldiers and police during a search for two American paratroopers missing in a Taliban-infested area of the country’s west.

The probe into a possible friendly fire incident further aggravates already strained relations between Afghan President Hamid Karzai and the international community, which holds his enfeebled government partly responsible for rising instability.

After enduring a drumbeat of criticism from world leaders in recent days, the Afghan government struck back on Saturday, saying it viewed a U.N. official’s prescription for ridding the country of corruption and warlords as an infringement on its national sovereignty.

The airstrike occurred Friday during heavy fighting in Badghis province, a remote area that borders Turkmenistan. Two days earlier, two American paratroopers disappeared there while trying to recover airdropped supplies that had fallen into a river. Fighting broke out between members of a search team and Taliban insurgents, the U.S. military said. Eight Afghans—four soldiers, three policemen and an interpreter—were killed. Seventeen Afghan troops, including soldiers and police, five American soldiers and another Afghan interpreter were wounded, the U.S. said.