The blast comes amid an unending wave of violence across Afghanistan.
Radio tempatan Salam Afghanistan mengatakan sekurang-kurangnya 10 orang terbunuh dalam serangan pengebom bunuh diri di Kementerian Pertahanan.
The Taliban says the defence ministry compound in Kabul was their target.
The blast appears to have occurred near Gulbahar Tower, which contains a shopping mall and residential units and is next to a government building.
General Sayed Mohammad Roshan Dil said the four attackers had been wearing police uniforms.
Calmness in war-raged Afghanistan for a few months was disrupted after an explosion hit Kabul central today killing 7 people.
"Some were against this concert, but we did not give up," she said. "We are all scared of suicide bombings, explosions, abductions and other issues in this country."
The latest grim assessment of Afghanistan's security situation comes as the US urgently seeks a way out of the 17-year war.
US President Donald Trump has been eager to end America's longest war and the Taliban have insisted on the withdrawal of foreign troops.
Taliban insurgents who claimed responsibility for the attack said they have killed 190 people in the complex attack.
Afghanistan was once a popular stop on the well-worn hippy trail between Europe and South Asia in the 1970s.
The explosion comes as diplomats ramp up efforts to end the 17-year war in Afghanistan, which by some estimates was the world's deadliest conflict in 2018.
Four militants, including the bomber, were killed and more than 350 people freed from the compound.
Plumes of black smoke could be seen rising from the compound, with at least two military helicopters circling above.
It is the bloodiest assault in the Afghan capital since a twin bomb attack on a wrestling club in September that killed at least 26 people.
KABUL: In the alley winding between the earthen walls of Old Kabul, Wakil Mohammad Saddeq insists on honouring his visitors with a cup of...
Afghan security forces say they shot dead a man who had been planning to blow himself up near supporters of Ahmad Shah Massoud.
The attack came as convoys of gun-wielding men terrorised Kabul as they commemorated the 17th anniversary of rebel leader's death.
Wilders said he would never personally stop his campaign against Islam but the risk to innocents, and of attacks on the Netherlands, stemming from the proposed contest were too great.
Dutch Prime Minister Mark Rutte has said that he does not support the planned contest but that he would defend Wilders' right to hold it.
Cross-border clashes are rare on Afghanistan's border with Tajikistan, compared, for example, with fighting along Afghanistan's eastern border with Pakistan.
A security official said the explosions were caused by rockets fired from outside the city, and some fell near the presidential palace, around embassy compounds and government buildings.
The attack on the training facility was the latest incident in a blood-soaked week that saw militants deliver crippling blows to government forces across Afghanistan.
There was no immediate claim of responsibility for the blast, which came after several weeks of relative calm in Kabul but previous attacks on Shi'ite targets in the area have been claimed by Islamic State.