Al Jazeera's Waliullah Shahin, reporting from Kabul, the capital, said that local residents refused to bury the dead until the Afghan government provided a "sufficient reason" for the operation.
Calls for assistance
Arsallah Jamal, the governor of Khost, had urged US forces to seek Afghan assistance before launching raids, saying that Afghans would be in a position to "reduce mistakes".
In the latest operation, US-led multinational forces said they were searching compounds for a fighter named Bismullah who organised roadside bomb attacks and smuggled weapons.
Military officials confirmed that an operation took place, reportedly aimed to "disrupt militant activities".
The troops had reportedly come under fire while searching for fighters suspected of carrying out bombings.
"Several armed militants were killed when they fired on coalition forces during the search. Coalition forces returned fire," a statement said.
"Coalition forces discovered a dead woman during a post-hostilities assessment in a building where one of the barricaded militants fired on coalition forces."
A dead child was discovered in a second compound, the statement said.
Two suspected fighters were detained in the raid.
In 2002, Hamid Karzai, the president, publicly and repeatedly accused the US of heavy-handedness in its operations.
The US military said that it has modified tactics over the years to cut down on civilian deaths.