President Karzai ordered the probe after local authorities said the attack in the eastern province of Kunar killed only civilians.
The province's chief of police, General Abdul Saboor Alayar, says the joint U.S. and Afghan raid disrupted a meeting of village elders.
He says the tribal elders were trying to resolve a longstanding legal dispute when the coalition soldiers attacked.
The province's governor and a number of other local officials say they have already started their investigation.
U.S. military spokesman Sergeant Chris Miller says a coalition inquiry also is under way to determine the victims' identities, but he says there is little question al-Qaida militants were involved.
"Afghan and coalition forces came under direct fire when approaching the compound, and defended themselves with return fire. All of the men killed were engaging Afghan and coalition forces with hostile fire," said Miller.
A U.S. statement issued after the attack confirmed a 10-year-old child was killed during the raid, which also recovered a number of grenades and other weapons.
President Karzai's decision Friday to order an investigation is the second time in less than a week that he has criticized the U.S. military.
The president has repeatedly urged the U.S.-led coalition to avoid civilian casualties as it hunts insurgents from the al-Qaida terrorist network and from the Taleban movement that once ruled Afghanistan.
U.S. officials say every precaution is taken to safeguard innocent lives.
On Saturday, a coalition spokesman confirmed that separate clashes in eastern and southern Afghanistan left two French coalition soldiers and at least seven Taleban insurgents dead.
The soldiers were killed Friday morning after their convoy hit a roadside bomb in Laghman Province, in the country's east. Two other soldiers were seriously wounded in the attack.