The deaths are expected to come up in meetings Mr. Karzai is scheduled to have with the American defense secretary, Robert M. Gates, who arrived in Afghanistan Monday.

Civilian casualties caused by NATO troops are corrosive to the relationship between the West and the Afghans, and reinforce the Taliban’s propaganda that NATO troops do not care about the Afghan people. In fact, far more civilians are killed by the insurgents than by NATO, according to the most recent United Nations report, which said that more than three-quarters of civilian casualties are now caused by the insurgents. However, those that are caused by NATO troops appear to reverberate more deeply because of underlying animosity about foreigners in the country.

In Kabul on Sunday, a protest took place over the death of the nine boys. A larger protest was held last week in Nanglam, the capital of the district where the killing took place.

The shootings occurred in a poor, mountainous area. A couple of the boys who died were the only males in their families and were responsible for the care of their mothers and sisters. The loss of the only male means that the women will have to rely on relatives, who usually are already overburdened with their own families.

A boy who was wounded but survived described a helicopter gunship that hunted down the children as they gathered wood on the mountainside outside their village. The gunners apparently mistook the children for insurgents who fired on an American base hours earlier.