A US military convoy near Kabul came under rocket fire late on Monday but the attackers missed their target and instead hit civilian cars, killing four Afghans, police said.
Three other civilians were wounded in the attack on a main road about 15km south of Kabul, the police chief in Logar province, Khan Mohammed, said on Tuesday.
He blamed the Taliban for the attack in the capital which is home to many foreigners.
Aljazeera correspondent in Afghanistan Samir Allawi said the civilians had been travelling from Kabul to the Maidan area. Allawi put the death toll at six people with three others injured.
According to the police, the civilian cars were travelling close behind five military Humvees when they were hit by two rockets and small-arms fire.
Included among the dead was a child, Mohammed added. The wounded were taken to hospitals in Kabul.
The police chief said extra security forces had been sent to the area and had surrounded a rundown fort where the suspects were thought to be hiding.
US military sergeant and spokeswoman for the US-led forces in Afghanistan Marina Evans said she had no details on the attack.
The city of four million is heavily guarded and has been spared much of the fighting that hit other parts of the country.
The Afghan Interior Ministry says it has started a vast search operation in nearby villages, Allawi reported.
The second attack happened hours later, just before dawn on Tuesday, when a police vehicle 50km east of Kabul, near a key trade route linking the capital with the eastern Pakistani border, was fired upon, said Ghafor Khan, a police spokesman in the eastern town of Jalalabad.
Rockets targeting a US convoy
hit the cars behind the Humvees
The attack killed a senior police officer who was a teacher at a police academy and wounded two others, he said.
The vehicle was riddled with bullets and destroyed, he said.
Khan said investigators suspected the victims were targeted because they "are teaching new police recruits and are crucial to bringing peace to our country".
Meanwhile police said they had discovered a major arms cache in Kabul.
The weapons discovered in Kabul were found in a junkyard for old military vehicles in the northern part of the city, said Interior Ministry spokesman Yousuf Stanekzai.
The explosives were made from old anti-personnel mines.