The U.S. military says it is investigating the reports but a spokesman said "if innocent people were killed in this operation, we apologize and express our condolences."
President Hamid Karzai has made an immediate demand of President-elect Barack Obama to prevent civilian casualties.
Kandahar province villager Abdul Jalil says he was hosting a wedding party for his niece when Taliban militants fighting U.S. forces took cover near his home. Jalil says 37 people were killed when U.S. warplanes later bombed the wedding party.
No Afghan officials could immediately confirm the number of casualties, which happened in a remote and dangerous part of Kandahar province. But Karzai referred to the incident at a news conference Wednesday held to congratulate Obama on his U.S. presidential election victory.
Karzai said he hopes the election will "bring peace to Afghanistan, life to Afghanistan and prosperity to the Afghan people and the rest of the world." He applauded America for its "courage" in electing Obama.
But he also used the occasion to immediately press Obama to find a way to prevent civilians casualties in operations by foreign forces. He then said airstrikes had caused deaths in the Shah Wali Kot district of Kandahar province.
"Our demand is that there will be no civilian casualties in Afghanistan. We cannot win the fight against terrorism with airstrikes," Karzai said. "This is my first demand of the new president of the United States - to put an end to civilian casualties."
The alleged airstrikes come only three months after the Afghan government found that a U.S. operation killed some 90 civilians in western Afghanistan. A U.S. report said 33 civilians died in that attack.
Another incident with a high number of civilian casualties could severely strain U.S.-Afghan relations.
Jalil said American forces came into his village late Monday night or Tuesday morning - after the bombing run - and searched the villagers and detained some of the men. Jalil said he told the Americans that they could search his grape orchards and his home but that they wouldn't find any militants.
"The Americans came and told us, 'You are sheltering the Taliban,' and I told the Americans 'Come inside and see for yourself, you are killing women and children,"' Jalil said. "After they saw that all the dead were civilians, they gave us permission to bury the bodies."
The U.S. military said it had sent personnel to the site to assess the situation and take appropriate action.
"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," Cmdr. Jeff Bender said in a statement. "If innocent people were killed in this operation, we apologize and express our condolences to the families and the people of Afghanistan."
Another witness to the bombing, Mohammad Nabi Khan, told AP at the main hospital in Kandahar city that two of his sons, ages 4 and 11, and his wife's brother were among the dead.
"What kind of security are the foreign troops providing in Afghanistan?" he asked.
Wedding parties in Afghanistan are segregated by gender, which explains why so many women and children could have died.
Civilian deaths have long caused friction between Karzai's government and the U.S. and NATO. But following the U.S. operation in western Afghanistan in August, relations between Afghanistan and the United States were seriously damaged. Karzai called for a review of operations by U.S. forces in Afghan villages.
An Afghan government commission found the Aug. 22 attack on the village of Aziziabad killed some 90 Afghan civilians - a finding backed by a preliminary U.N. report. The U.S. military at first said only 30 militants were killed and no civilians. But days later the military said up to seven civilians had died.
However, after video of Azizabad emerged days later showing what appeared to be dozens of bodies, the U.S. appointed a U.S.-based one-star general to investigate. His report found the U.S. operation killed 33 civilians. The report said U.S. troops were justified in firing on the village because militants had first fired on them and wounded a U.S. soldier.
Karzai, speaking on the grounds of the presidential palace in Kabul, said "race, color and ethnicity" will disappear as a factor in politics around the world because of Obama's election.
He used the occasion to press the U.S. government to "take the fight (to) where the training centers and the resources of the terrorists are," a reference to Pakistan's lawless tribal areas.
Obama has said that if he is elected, he could launch unilateral attacks on high-value terrorist targets in Pakistan as they become exposed and "if Pakistan cannot or will not act" against them.