Tensions ahead of pullout
Afghanistan's National Security Council, chaired by Karzai, recently accused "armed individuals named as U.S. special force" of torturing and murdering innocent people in Wardak province. The government demanded members of the elite U.S. military units leave the province west of Kabul.
But the council also said the United States rejected such suggestions.
U.S. military officials said all allegations of misconduct are taken seriously, and that the military was looking into the allegation.
Last year, Karzai called for U.S. troops to pull out of outposts in Afghan villages and return to their main bases.
In October, he complained the United States was failing to supply Afghan forces with weapons needed to fight insurgents.
Then-U.S. Defense Secretary Leon Panetta responded at the time that "it would be helpful if (Karzai), every once in a while, expressed his thanks for the sacrifices that have been made by those who have fought and died for Afghanistan, rather than criticizing them."
The Obama administration is making decisions about bringing troops home.
In January, Panetta reiterated his opposition to pulling out all U.S. troops by 2014, saying it would take away negotiating leverage with the Taliban.
"The stronger position we take about staying, the better chances we have to ultimately reach political reconciliation," Panetta told journalists.