"Today, just after 4.30pm (1200 GMT), a man riding on a motorbike carried out a suicide attack in front of the Kabul military training centre," Defence Ministry spokesman Mohammed Zahir Azimi said on Wednesday.
"Our initial reports suggest that nine people have been killed and 28 wounded. Four of the nine killed are Afghan National Army soldiers and the rest are under investigation," he said.
He said the bomber was wearing a military uniform.
The Taliban claimed responsibility for the attack and warned that more could be expected.
Azimi said most of the dead were army officers. Another ministry official said eight of the dead were soldiers and another was a civilian.
Four minibuses that had been carrying soldiers were burned in the attack, witnesses said.
Major Andy Elmes, a spokesman for the Nato-led International Security Assistance Force (ISAF) peacekeepers, said it had rushed teams to help treat and evacuate casualties.
Taliban spokesman Abdul Latif Hakimi named the bomber as Kabul resident Sardar Mohammad and warned that the insurgents planned more such attacks.
"More mujahidin suiciders are ready to follow his way and you will witness them doing it in the future," he said by satellite phone from an undisclosed location.
"More mujahidin suiciders are ready to follow his way and you will witness them doing it in the future"
Abdul Latif Hakimi,
Although the Taliban failed in their vow to derail the 18 September elections for a national assembly and provincial councils, violence has picked up since the vote.
The blast in northern Kabul is the first major attack in Afghanistan since the war-scarred country held landmark parliamentary elections this month and follows a period of calm in the city.
A Western military source speaking on condition of anonymity said the victims were all Afghans and none were serving with either the US military or with the Nato-led peacekeeping force in Afghanistan.
Dozens of peacekeepers had been deployed near the site of the blast.
Elsewhere in Afghanistan, bomb blasts also killed three people and wounded five, including a Bangladeshi UN worker.
Two police officers and a civilian died and four civilians were wounded in a suspected mine blast in the eastern province of Kunar on Wednesday, police said, adding that the device may have been planted by the Taliban.
A Bangladeshi engineer working with the UN Office for Project Services was critically wounded by a roadside bomb on Tuesday while travelling in a convoy in adjacent Nangarhar province, a UN official said.
He was taken for treatment to the US military base in Bagram, north of Kabul, said UN spokesman Samuel Hendricks.
More than 1000 people have died in intensified violence this year, the bloodiest period since US-led forces overthrew the Taliban in 2001.
Meanwhile, Afghan Interior Minister Ali Ahmad Jalali denied on Wednesday his decision to resign was due to disputes with President Hamid Karzai, but said there was a need to purge corrupt officials and those involved in the drugs trade.
Jalali announced on Tuesday that he was stepping down, sparking a flurry of speculation that he had fallen out with Karzai over provincial officials' links to the opium trade.
Jalali (above) denied his stepping
down was due to a rift with Karzai
At a news conference on Wednesday, he denied he had fallen out with the US-backed president, but said his decision was final.
"The rumours regarding my resignation as reported by the press over disagreements with His Excellency Karzai are baseless," Jalali said, reiterating that he wanted to return to academic life.
At the same time, he stressed the need to rid the government of corruption and officials involved in the drugs trade.
"Without that, we will not be able to bring about a healthy, committed administration that will only serve the people, that will deliver to the people what they are supposed to deliver."
Afghanistan is the world's biggest producer of opium and its derivative heroin, and analysts describe the trade as the biggest obstacle to stability.