Tuesday’s bombing happened during the morning rush hour in a residential neighborhood close to the ministry of defence and military compounds.
There are unverified claims that Taliban fighters managed to breach the defences of the National Directorate of Security, the main spy agency which protects high-ranking government officials.
The “blast was carried out by a suicide bomber in a car and possibly one or two bombers are still resisting”, Mr Sediqqi was quoted as said.
“The scene of the attack has been completely cordoned off by Afghan security forces.”
Several people have been killed and more than 200 have been injured in a huge explosion in the centre of the Afghan capital Kabul, officials say.
Interior ministry spokesman Sediq Sediqqi said a suicide attacker had detonated a vehicle. Gunfire can still be heard.
A Taliban spokesman said the group carried out the attack.
It comes a week after it said it was launching its “spring offensive”, warning of “large-scale attacks”.