Nato's International security assistance force (Isaf) said it had dispatched a quick reaction force to the area outside the American embassy and near Afghan and US army bases in the centre of Kabul.
Saleh Ahmed, a local resident in Kabul, said the accident happend when the civilian vehicle attempted to drive onto the main road from a side street and was hit by one of the two SUVs.
"The civilian vehicle was trying to get into the main road when the two foreign vehicles hit it and killed all four occupants," Ahmed said.
"People gathered around the crash site to see what happened, got angry and started attacking the foreigners."
Security forces were concerned that the deadly traffic accident could lead to widespread rioting, our correspondent said.
A similar accident in May 2006 led to massive riots in Kabul that left at least 14 people dead.
The area "seems to have calmed down for now, but authorities are very concerned", our correspondent said.
Outside of the capital, six US soldiers were killed in a series of attacks in Afghanistan, bringing this month's death toll to at least 66, making July the deadliest month for American forces in nearly nine years of war.
In southern Afghanistan, one US soldier died following an insurgent attack and two others were killed in a roadside bombing on Friday, the US military said.
Earlier on Friday, Nato said that three service members died in southern Afghanistan on Thursday.
The statement did not provide the nationalities of the dead, but US officials speaking on the condition of anonymity said all three were Americans.
June had previously been the deadliest month for US troops as well as the overall Nato led force.
A total of 104 international troops died in June, including 60 Americans, according to a tally compiled by Associated Press.