Afghanistan violence: Deadly suicide bomb hits Kabul
A suicide attacker detonated a vehicle and gunmen stormed the area, reports say. Officials say the gunfight is now over and the area has been cleared.
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.
Tuesday's bombing happened during the morning rush hour in Pul-e-Mahmud, a busy neighbourhood where homes, mosques, schools and businesses nestle close to the Ministry of Defence, other ministries and military compounds.
Soldiers and security officers are reported to be among the casualties, but the majority are civilians, says the BBC Afghan Service's Waheed Massoud.
The blast shattered windows up to 1.6km (one mile) away. The Associated Press quoted a police officer as saying it was one of the most powerful explosions he had ever heard, and he could not see or hear anything for 20 minutes after.
It appears the initial blast cleared the way for Taliban fighters to enter the area - a commonly used tactic.
Unconfirmed claims suggest they managed to breach the defences of the National Directorate of Security, the main spy agency which protects high-ranking government officials.
The presidential palace - only a few hundred metres from the blast - condemned the attack "in the strongest possible terms".
"Such cowardly terrorist attacks will not weaken the will and determination of Afghan security forces to fight against terrorism."
A tweet from President Ghani's office's official account suggested the attack "clearly shows the enemy's defeat in face-to-face battle with ANSDF" - the Afghan National Security and Defense Forces.
But correspondents say that in fact the Taliban has gained in strength since the bulk of British, American and other Nato forces left in 2014.
It has also been buoyed by and a flood of foreign fighters joining its ranks, and now controls sizeable parts of Afghanistan.
( Source )