The 45-seater bus was destroyed in the blast outside the police headquarters in a crowded part of the city centre near a busy market.
Two minibuses were also badly damaged and witnesses said bystanders may have been hit. The bomb exploded during peak-hour traffic.
Samir Allawi, Al Jazeera's Afghanistan bureau chief, said four foreigners, believed to be police trainers, were among the dead.
The interior ministry said that those reports were incorrect but two Japanese, a Korean and two Pakistanis had been wounded.
Hamid Karzai, Afghanistan's president, condemned the attack, saying it was an attempt to block the training of the police force.
The Taliban, forced from government by US-led forces in 2001, said it carried out the blast. If the toll is confirmed it will be the most deadly suicide attack in Kabul.
A spokesman said the bomber was 25-year-old Mullah Asim.
"We take the responsibility. It was a suicide car bomb," Zabihullah Mujahid said.
|"We have plans for more successful attacks in future" |
Mullah Hayatullah Khan,
Mullah Hayatullah Khan, a Taliban commander, said: "It was a very, very successful suicide attack".
"We have plans for more successful attacks in future," he said.
The Taliban has been fighting against Nato and US forces for the past five years and has carried out a series of recent suicide bomb attacks.
Since Friday, there have been attacks in the south, centre and north of the country, including a blast in Kabul on Saturday.
The Pakistan-based Afghan Islamic Press quoted a Taliban spokesman as saying: "The operation was 100 per cent successful as we hit our target and that was police."
Later on Sunday, a roadside bomb in southern Afghanistan killed three foreign soldiers and an interpreter.
"Three coalition servicemembers and an Afghan interpreter were killed in an improvised explosive device detonation in Kandahar province," Sergeant First Class Dean Welch coalition spokesman, said.