The reported airstrike happened Monday in the Shah Wali Kott district of Afghanistan's southern Kandahar province, the military said in a news release.
The Associated Press, quoting a villager at the scene, reported that 33 women and children -- all members of a wedding party -- were killed during a U.S. fight with the Taliban.
"The coalition and Afghan authorities are investigating reports of non-combatant casualties in the village of Wech Baghtu," said U.S military spokesman Cmdr. Jeff Bender.
"Though facts are unclear at this point, we take very seriously our responsibility to protect the people of Afghanistan and to avoid circumstances where noncombatant civilians are placed at risk."
"If innocent people were killed in this operation, we apologize and express our condolences to the families and the people of Afghanistan," Bender said. "We have dispatched coalition personnel to the site to quickly assess the situation and take actions as appropriate."
President Karzai demanded U.S. election winner Barack Obama to limit further civilian casualties. The Afghan leader has previously condemned the U.S. military over attacks in which scores of civilians have perished.
"Our demand is that there will be no civilian casualties in Afghanistan. We cannot win the fight against terrorism with air strikes," Karzai said. "This is my first demand of the new president of the United States -- to put an end to civilian casualties."
Taliban spokesman Qari Mohammad Yousif Ahmadi said militants engaged in an firefight with "enemy forces" from Monday until early Wednesday that killed 13 soldiers and one Taliban fighter.
During the firefight, airstrikes were called in, leading to the 35 civilian deaths and 15 civilians wounded, the Taliban spokesman said.
Wali Karzai, the head of the Kandahar provincial council and Karzai's brother confirmed that "some civilians were killed and wounded in airstrike by foreign forces in Shah Wali Kot district, but we don't know how many."
He said the aerial bombardment was conducted after the joint Afghan and foreign forces were attacked by militants in the area.
Relations between the United States and Afghanistan were strained earlier this year when a U.S. airstrike in late August killed dozens of civilians in the Shindand District of the western Afghan province of Herat.
Afghan and United Nations officials said 90 civilians, mostly women and children, were killed in the August 22 strike.
The U.S. military initially denied any civilians were killed but a subsequent investigation prompted by cell phone pictures showing dozens of bodies conceded that 33 civilians were killed.
Weeks after the deadly strike, U.S. Secretary of Defense Robert Gates traveled to Kabul, where he met with Karzai and publicly apologized for the incident.
In another development, a soldier with the NATO-led coalition in Afghanistan was killed Tuesday when his patrol came under attack in the southern part of the country, NATO's International Security Assistance Force said.