A spokesman for the ousted Taleban said militants from the group carried out the attack late Monday and one in the east of the country on Tuesday, which officials said killed a policeman.
Three other civilians were wounded in the attack on the convoy travelling about 45 kilometres (28 miles) south-east of Kabul in Logar province, interior ministry spokesman Yousuf Stanizai said.
"Six of our countrymen were killed and three others were wounded," he said.
The target was a vehicle of the US-led coalition force in Afghanistan, he said. Afghan police had sealed off the area and were looking for the attackers.
The coalition said an improvised bomb had hit the last vehicle in a US convoy in the province.
"They moved out of the area immediately," spokeswoman Sergeant Marina Evans said. "The IED (improvised explosive device) or some subsequent action must have caused the civilian casualties," she said.
A Taleban spokesman, Mohammad Anif, said by telephone: "We attacked a US convoy in Logar. There was an exchange of fire - we retreated." He could not comment on casualties.