At the side of the road, foreign troops gave first-aid to some blood-stained fellow soldiers from the convoy, but the nationality of those involved was unclear.
The explosion occurred near the main entrance to the heavily fortified US embassy at about 8:00 am (0900 IST) during heavy rush-hour traffic, with several people badly wounded, an AFP photographer at the scene said.
One vehicle from the convoy was thrown off the road and destroyed by the blast, which was also close to the Supreme Court and a military base.
"It was a suicide car bomber targeting a foreign forces convoy along the airport road," Farid Afzali, chief of the city's police investigation department, told AFP.
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The Taliban quickly claimed responsibility via a recognised Twitter account.
The two presidential candidates in the election yesterday held talks on ending the deadlock over who won the election to replace President Hamid Karzai, who has ruled since the fall of the Taliban.
Ashraf Ghani and Abdullah Abdullah have been wrangling over a power-sharing deal after the vote was engulfed in allegations of massive fraud that have threatened to spark instability as US-led NATO troops pull out of the country.
Aimal Faizi, spokesman for Karzai, declined to give details of the agreement, which both campaign teams have previously said would hinge on the power held by a new chief executive officer (CEO), who would be nominated by the election loser.
The stand-off has threatened to wreck hopes that the US-led military and civilian aid effort since the fall of the Taliban regime in 2001 would leave Afghanistan as a democratic country.