"This morning a convoy of British troops were passing here and they had a misunderstanding with a civilian vehicle. The troops opened fire and killed one civilian and wounded three more," Mohammad Ayoub Salangi, Kabul's police chief, told Reuters news agency.
But the International Security Assistance Force (Isaf) disputed the claim that its troops had opened fire, saying the incident had been a traffic accident.
Traffic accident
The US-led coalition said that it regretted the accident, in which one of its vehicles had been hit by a civilian minivan that then crashed into a roadside shop, causing the casulaties.
Crowds chanted "death to Bush, death to America" as the body of the victim was put into the back of a taxi and driven away from the scene.
"They killed my son, my son is dead," said a weeping old man.
The rioters pelted Afghan police with stones and were chased down side-streets before dispersing.
Taliban ambush
Meanwhile, an Afghan official said that Taliban fighters had killed 13 Afghan soldiers and captured 16 others in an ambush in a northwestern province.
Abdul Ghani Sabri, a deputy provincial governor, said seven Taliban were also killed during the battle in Bala Murghab district of Badghis province on Thursday night.
In another attack, a former spokesman for the Taliban was shot dead by fighters wearing Afghan police uniforms at midnight on Thursday, officials and relatives said.
Abdul Haq Daqiq, who was known as Doctor Mohammd Hanif while he was spokesman for the Taliban around 2006, was killed in his home in the eastern province of Nangarhar.
Three family members were also shot.
The Taliban said they no longer had contact with Hanif. The motive for the killing was unclear, but locals said it could have been linked to a family feud.
On Thursday, at least seven people were reported killed and 16 injured in a large explosion near the US embassy in Kabul.
Officials suspect it was a suicide attack that targeted a convoy of foreign troops close to the embassy entrance.
The Taliban has claimed responsibility for the attack.