Two American soldiers are confirmed to be among those killed.
The Taliban later claimed responsibility for the Friday morning blast.
Mohammed Haneef, a Taliban spokesman, told an Aljazeera correspondent in Islamabad that the suicide attack was carried by Shah Wali, from Nangrahar province, eastern Afghanistan.
The United States has condemned the suicide car bomb blast in the Afghan capital calling it "a heinous act of terrorism".
The Taliban militia that is waging a guerrilla-style insurgency claimed responsibility for the suicide attack on a US military convoy, one of the deadliest attacks to hit the heavily secured Kabul city.
"It's a heinous act of terrorism that we condemn," state department spokesman Sean McCormack told said on Saturday.
"Certainly we will work with the Afghan government to determine who perpetrated this act of terrorism and work to bring to justice any of those who were associated with this act," he said.
A journalist saw two bodies being carried away from the crowded area in an ambulance, and body parts scattered around the site of the explosion in the city centre.
A policeman at the scene said he feared the number of casualties could be "very high".
Reports said the car that had carried the bomb was split into two and was in flames.
Rubble was flung about 50 metres from the site, about 100 metres from the embassy.
Hamidullah, a traffic policemen, said: "It was a huge explosion. Suddenly everything got dark. I lay down. When I stood up I saw two of my colleagues were wounded."