Pakistan has said the attack was an unprovoked assault.
The Nato-led coalition in Afghanistan has made little comment, apart from offering condolences for the deaths and admitting it was “highly likely” they had been caused by its forces.
“They came under cross-border fire,” the Western official said.
The Afghan official said troops had come under fire from inside Pakistan as they were descending from helicopters, which had returned fire.
Both officials asked not to be named because the attack is so sensitive.
It has severely strained already fractious relations between the United States and Islamabad.
Protests erupt across Pakistan
Thousands gathered outside the United States (US) consulate in Karachi on Sunday to protest against the cross-border air attack.
A Reuters reporter at the scene said the angry crowd shouted “Down with America”. One young man climbed on the wall surrounding the heavily fortified compound and attached a Pakistani flag to barbed wire.
“America is attacking our borders. The government should immediately break ties with it,” said Naseema Baluch, a housewife attending the Karachi demonstration.
“America wants to occupy our country but we will not let it do that.”
About 500 members of Jamaat-e-Islami staged a protest in Mohmand, where the NATO attack took place.
“Jihad is the only answer to America”, they yelled.
