The attack comes when a Taliban delegation and US representatives are carrying out the seventh round of meetings in Qatar to discuss peace negotiations in Afghanistan.
A witness told Xinhua news agency that militants entered an under-construction building in the morning in the high security Pul-i-Mahmoud Khan area of Kabul and exchanged fire with the security forces who reached the site to control the situation.
According to the witness, the militants first detonated their explosives-laden car and then began firing.
The area targeted is close to a branch of the the Defence Ministry building, a sports stadium, a branch of the Information and Culture Ministry and houses.
The Taliban claimed responsibility for the bombing in a statement, saying that the target had been the logistics and engineering department of the Ministry of Defence, Efe news reported.
The initial explosion at the entrance opened the way for insurgents to enter the building and target the personnel inside, according to the statement. It claimed that several soldiers and Defence Ministry officials had been killed so far and that the attack was still underway.
Following the explosion, which could be heard several kilometres away, a huge rising column of smoke could be seen.
Defence Ministry vice-spokesperson Fawad Aman told Efe that the attack occurred near the Ministry's logistics and engineering department.
Facilities located near the site of the bombing include the headquarters of Shamshad TV where several of its employees were injured in the explosion, said one of its journalists.
The incident comes as American and Taliban negotiators are meeting in Qatar amid hopes for a deal on an American troop withdrawal from Afghanistan.
Both sides are seeking a way out of nearly two decades of armed conflict in the nation, although, so far the Taliban have refused to negotiate with the Afghan government.
( With inputs from IANS )