Investigations showed the late Wednesday night raid in an area of southeastern Khost had resulted in "killing two males, two females and wounding two females. There are reports of an infant also killed," the military said in a statement.
"We deeply regret the tragic loss of life in this precious family," the late Thursday statement quoted Brigadier General Michael Ryan of the U.S. forces as saying.
"Words alone cannot begin to express our regret and sympathy and we will ensure the surviving family members are properly cared for."
Civilian casualties caused by foreign forces hunting militants have sapped support for the presence of the troops in Afghanistan more than seven years since a U.S.-led invasion overthrew the Taliban from power.
The casualties have also been a major source of friction between the Afghan government and the West.
The father of a seven-day-old boy said on Thursday his infant son died in the raid. A female school teacher was also killed and the child's mother wounded, the father said.
Hundreds of civilians were killed in operations by Afghan and foreign forces last year alone in Afghanistan, according to human right groups and the Afghan government.
Violence in Afghanistan has reached its highest level since the U.S.-led invasion despite a growing number of foreign troops and has spread from the south and east to the outskirts of the capital, Kabul.