The strike, near Kabul airport, killed 10 members of one family, including six children, relatives have told the BBC.
The US military said it was targeting a vehicle carrying at least one person associated with the Afghan branch of the Islamic State group.
The US was assessing and investigating reports of civilian deaths, it added.
American commanders said there were "significant secondary explosions" after the drone strike - implying there were explosives at the scene - which may have harmed people nearby.
The youngest child to be killed was two-year-old Sumaya, and the oldest child was 12-year-old Farzad, the family told the BBC.
"It's wrong, it's a brutal attack, and it's happened based on wrong information," Ramin Yousufi, a relative of the victims, said.
He added, tearfully: "Why have they killed our family? Our children? They are so burned out we cannot identify their bodies, their faces."
Another relative, Emal Ahmadi, told the BBC that it was his two-year-old daughter who was killed in the strike.
Mr Ahmadi said he and others in the family had applied for evacuation to the US, and had been waiting for a phone call telling them to go to the airport.
That included one of his relatives, Ahmad Naser, who was killed in the strike and had previously worked as a translator with US forces. Other victims had previously worked for international organisations and held visas allowing them entry to the US.
The US, Mr Ahmadi added, had made "a mistake, it was a big mistake".
Pentagon press secretary John Kirby said the US was "not in a position to dispute" the reports.
"Make no mistake, no military on the face of the Earth works harder to avoid civilian casualties than the United States' military, and nobody wants to see innocent life taken," he said.
"We take it very, very seriously and when we know that we have caused innocent life to be lost in the conduct of our operations, we're transparent about it."
He then defended the intelligence about "what we believed to be a very real, a very specific and a very imminent threat" against Kabul's Hamad Karzai International airport from IS-K (Islamic State Khorasan Province), IS's Afghan affiliate.