A suicide bomber destroyed a civilian vehicle about five kilometres (three miles) from the country's largest US military base at the small town of Bagram, 50 kilometres north of Kabul, the interior ministry said.
Six people from the same family were killed, including two children, it said in a statement. Another child was wounded, it said.
"Two men, two women and two children are killed," ministry spokesman Zemarai Bashary told AFP separately. "This is an act of insurgents," he said.
Such attacks are usually directed at Afghan or Western security forces who are trying to put down a Taliban-led insurgency.
A US soldier was killed and two wounded in an insurgent attack in the eastern province of Paktya, which border Pakistan, the US military said.
Paktya province spokesman, Rohullah Samoon, said an Afghan interpreter was killed in the same incident. A roadside bomb had hit a military vehicle, he said.
Another roadside bomb struck a vehicle carrying private Afghan guards in the same province and killed eight of the men, he said. The guards were contracted to the international military forces, Samoon said.
The British Ministry of Defence announced in London its troops had killed a senior Taliban leader in the southern province of Helmand, who was behind suicide bomb attacks that have killed several British soldiers.
"UK forces conducted a successful precision strike against one of the most dangerous men in Helmand, and what we consider to be the most dangerous man in the central area around (provincial capital) Lashkar Gah," Lieutenant Colonel Nick Richardson said.
The Helmand government confirmed that a commander named Akhtar Mohammad Mansur was killed. Officials could however not say if he was the militant of the same name who is one of the militia's top commanders.
To the west, Taliban fighters attacked a convoy in the province of Farah, killing 18 Afghan private security guards, deputy provincial governor Mohammad Younus Rasouli said.
Police said earlier more than 10 guards were killed and 10 vehicles destroyed.
In the adjoining province of Nimroz, Taliban attacked a police post on Tuesday and killed two policemen, provincial police chief Abdul Jabar Pordeli said.
The US military said meanwhile troops had killed 12 militants in operations in the eastern province of Paktika and in Wardak, near Kabul, where four US soldiers were killed in bomb blasts on Monday.
Two more militants were killed after attacking Afghan troops in the Uzbin Valley northeast of Kabul, a NATO military spokesman said.
Fighting has escalated across Afghanistan, where at least a dozen people, including insurgents, have been reported killed almost daily in past weeks.
The violence is likely to raise concerns about stability in the vast, predominantly rural country ahead of key presidential and provincial elections on August 20 for which Western countries have pledged thousands more troops.
The Taliban were in government from 1996 until 2001, when they were removed by a US-led invasion after the September 11 attacks on the United States, for sheltering Al-Qaeda.
The extremists were able to regroup, some in sanctuaries across the border in Pakistan, to launch an increasingly deadly insurgency.
Concern about worsening security has led the United States to deploy 17,000 extra combat troops, most of them in the southern and western areas of the country.