The attack comes a week after a suicide car bomb targeting a foreign military convoy killed 15 people including five Americans in the deadliest attack in the Afghan capital for nearly a year.
The Taliban announced their annual "spring offensive" on April 27, opening a crucial period as local security forces take the lead in the fight against the insurgents.
At least two blasts hit the centre of Kabul at about 4:00 pm (1130 GMT) today, the second day of the Afghan weekend, and gunfire erupted as security forces rushed to the scene.
Kabul police spokesman Hashmat Stanikzai told AFP the initial blast came close to a hospital run by the NDS intelligence agency and the headquarters of the Afghan Public Protection Force (APPF), a government force that provides security for clients including international firms, supply convoys and aid groups.
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He said gunmen had occupied a building in the attack, which is ongoing.
Jawed Kazem, a local shopkeeper, said: "I was sitting in my shop when the explosion happened. It was a big explosion which threw me off my chair, minutes later another explosion happened.
Taliban spokesman Zabiullah Mujahid told AFP that his group was responsible and added that the attack began with a suicide car bombing.
"A group of other mujahideen armed with heavy and light weapons then took position in a building and are firing on several targets including a building in which the foreigners and members of spy agency stay," he said.
The suicide bombing last Thursday was the first major attack in Kabul since March 9 when a bomber on a bicycle killed nine people outside the defence ministry during a visit by US Defense Secretary Chuck Hagel.