A suicide bomber has slammed his explosives-packed Toyota Corolla into two armoured cars carrying US troops and civilians through Kabul, killing six of the people inside the vehicles and nine Afghan civilian passersby.

Two schoolchildren were among the dead, and a further 39 people were injured when the blast ripped through Thursday morning rush-hour traffic, sending shrapnel slicing through dozens of civilian vehicles.

The explosion was heard miles away on the other side of the city, and sent a thick column of white smoke into the air.

"Around 8 o'clock this morning, two vehicles belonging to foreign advisers were bombed by a Corolla. They were badly damaged, along with 10 civilian cars, and another 20 vehicles in the area were lightly damaged," said Kabul police chief Ayoub Salangi.

The attack, near a stadium where the Taliban once carried out public executions, is the deadliest in Kabul this year. A suicide bomber last struck just over two months ago, killing nine Afghan civilians outside the defence ministry during a visit by the US defence secretary, Chuck Hagel.

Since then Afghan security forces say they have foiled a string of plots to attack the capital, including finding an eight-tonne truck bomb on the outskirts of Kabul. But Thursday's bloodshed, in an area near the heart of the city and its heavily militarised diplomatic and government core, is a reminder of the insurgency's reach.

The attack was claimed by a Taliban-linked group headed by Gulbuddin Hekmatyar, a former mujahideen commander who once received US funding to fight Soviet forces. A spokesman for Hizb-e-Islami, Haroon Zarghoon, said a newly formed suicide squad had attacked American advisers working in the city, after watching them for days.

"The cell had been monitoring the movement and timing of the American convoy for a week and implemented the plan Thursday morning," Zarghoon told the Associated Press. About eight months ago the group killed 12 people in a suicide attack on a minibus carrying foreign pilots to Kabul airport.

The US military confirmed that two of its soldiers were killed in the blast. The Nato-led coalition said four civilians it employed also died, but declined to comment on whether there were any injured survivors.

The remains of one of their vehicles was still at the site several hours after the blast, tonnes of reinforced steel so twisted and lacerated it would have been impossible for anyone inside to escape. However, it was not clear what happened to the second vehicle, which must have carried at least one of the dead as SUVs cannot usually fit more than five people.

The bomber used a model of car so ubiquitous in Kabul that street vendors sell windscreen wipers and other spare parts at junctions. He would have been almost impossible to pick out from the morning crowds in a part of the city where few foreigners travel regularly.

By contrast the armoured vehicles used by most diplomats and military officers, as well as senior Afghan officials, stick out as sleek, heavy targets in the city's swarms of mostly battered vehicles. Many remove their number plates or boast illegal blacked out windows to try and conceal the high-profile passengers inside.

President Hamid Karzai condemned the attack as a "cowardly act of terror … [that]brutally targeted a residential area", but did not directly denounce Hizb-e-Islami. Karzai, who is pushing hard for peace talks and has reached out to the Taliban as errant "brothers", ascribed the attack only to "enemies who don't want to see the Afghan Muslim nation live in peace".

The top US and Nato commander in Afghanistan, General Joseph Dunford, described the bombing as "desperate and indiscriminate", but denied it was a sign of Taliban strength.

"While today's attack shows the insurgents remain dangerous, they are not a threat to the Afghan government and its forces," he said.

Additional reporting by Mokhtar Amiri