Five militants were involved, three of whom have been killed, he said.
The attack has now been claimed by the Islamic State, according to the militant group's Amaq news agency.
It comes days after the deadliest bombing for months hit Kabul when an ambulance packed with explosives killed at least 100 people.
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09:07
Heavy gunfire and explosions have been heard at a military academy in the Afghan capital, Kabul.
The Marshal Fahim National Defense University came under attack early Monday morning, reports said.
It comes days after the deadliest bombing for months hit Kabul when an ambulance packed with explosives killed at least 100 people.
Islamic State and the Taliban have recently carried out attacks in the city.
Several explosions were heard, as well as small arms fire, as the attack began at about 05:00 local time (00:30 GMT), the BBC's Mahfouz Zubaide reported from Kabul.
Security forces have blocked off all roads in the area, Afghan media outlet Tolo said.
According to Tolo, the president's spokesperson has confirmed the attack, saying that none of the attackers had been able to get further than the first gate.
News agency AFP cited a police spokesman confirming rocket and gunfire but saying it was now calm.
According to Reuters, police said there had been an incident inside at a military site but said it was not clear if it was an attack by militants.
Reports say some of the gunmen have been killed in the attack.
BBC
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