The attack comes just hours after a suicide bomber detonated explosives inside an education centre in western Kabul, where students were studying for college entrance exams, killing at least 37 people.
Military and intelligence facilities in Kabul have been regularly targeted by insurgents. Numerous casualties were students between ages of 16 and 18.
The blast comes less than a day after a Taliban attack in northern Afghanistan killed more than 30 police officers and soldiers, and less than a week after the Taliban launched a surprise attack on the city of Ghazni.
According to reports, a number of gunmen have launched a coordinated attack on a security compound close to Qambar Square.
Afghan forces appeared to have finally pushed Taliban fighters from the strategic provincial capital, as the United Nations warned that reports suggested up to 150 civilians might have been killed in the fighting.
Afghan President Ashraf Ghani condemned the "terrorist" attack that "martyred and wounded the innocent" - students attending class - and ordered an investigation into the attack.
No one has so far claimed responsibility for the bombing but officials blame the Islamic State group, which considers Shiites to be heretics and frequently targets them, attacking their mosques, schools and cultural centers.
With parliamentary elections due on October 20, authorities had been bracing for more attacks in Kabul and other cities, but even so, the scale of the violence has come as a shock to a government facing bitter criticism over its handling of the war.
Mohammad Safdar Mohseni, head of the provincial council, reportedly said the Taliban fighters set fire to checkpoints after they waged their attack in the Baghlan-i Markazi district.
"It took Afghan forces - assisted by USA advisors - five days to repel the insurgents", NPR's Diaa Hadid reports.
"It also showed how militants are still able to stage large-scale attacks, even in the heart of Kabul, and underscored the struggles of the Afghan forces to provide security and stability on their own". The assault on Ghazni was widely seen as a show of force ahead of possible peace talks with the US, which has been at war in Afghanistan for almost 17 years. And six young girls were killed after playing with an unexploded rocket shell, an official in the eastern province of Laghman told the wire service.
The Taliban have not claimed a major assault in Kabul for weeks.
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