KABUL, Afghanistan - An Afghan provincial governor said yesterday that an apparent U.S. air strike killed 10 Afghan civilians, and an immediate investigation was ordered by President Hamid Karzai, who has harshly criticized such incidents in the past.

If the reports are borne out, it would be the most serious instance in months of Western forces mistakenly killing Afghan civilians.

Civilian casualties at the hands of foreign forces have fallen off dramatically in the last six months, after Army Gen. Stanley A. McChrystal, the top commander of U.S. and allied forces in Afghanistan, issued strict new rules of engagement limiting the use of force if noncombatants are thought to be in the area.

The alleged incident took place Sunday in a remote area of Kunar province, in Afghanistan's northeast. Tribal elders in the district of Narang first reported the deaths, and the Associated Press reported that eight of those killed were students.

Karzai's office, in a brief statement, condemned the deaths and promised an investigation but provided no details about the circumstances.

Civilian casualties have long been a sore point between Karzai's government and the Western military. McChrystal's directive was issued after a spike in deaths and injuries among noncombatants. The general told field commanders then that protecting civilian lives must be their top priority because in Afghanistan's tight-knit tribal society, such casualties inflame anger against foreign troops, undermining their mission and bringing new recruits to the insurgency.

Nearly all the foreign forces operating in Kunar province, where the latest reported deaths took place, are American. U.S. military officials and NATO's International Security Assistance Force said they were checking on the reports from Kunar but had no immediate comment.

Western military officials reported a new outbreak of fighting in the country's northwest, in Baghdis province. There, they said, about 60 militants, with rocket-propelled grenades and assault rifles, attacked coalition forces defending outposts belonging to the Afghan police and army.

Building up the Afghan security forces is a key element of the Obama administration's plan for an eventual drawdown of Western troops in Afghanistan. But both the police and army are undertrained and undermanned, and the police in particular suffer heavy casualties because insurgents regard them as a "soft" target.