The Taliban stormed two small bases in northern Baghlan province on Wednesday, killing dozens of Afghan troops and police officers - the latest in a string of battlefield successes by the guerrillas, officials said.
In recent months, the Taliban have seized several districts across Afghanistan, staging near-daily attacks on security forces, but they have been unable to capture and hold urban areas.
Jawad Ghawari, a member of the city's Shia clerical council, blamed Islamic State (IS) for the attack, which carried all the hallmarks of past assaults on Shia mosques, schools and cultural centres.
Frequent terror attacks in the war-torn country hit facilities of government and security forces, as well as so-called soft targets where many people gather.
Around a dozen ambulances rushed to the Mawoud education centre in the western part of the city, where students and relatives described pulling bloodied victims from the rubble of a classroom that had been crowded with teenagers preparing to go to university.
A spokesman for the USA military, Lt. Col. Martin O'Donnell, said the city "remains under Afghan government control, and the isolated and disparate Taliban forces remaining in the city do not pose a threat to its collapse, as some have claimed".
"They were facing severe shortage of food and drinking water as the power supply was also suspended to the city two days ago", the Taliban commander, who declined to be identified, said by telephone.
The local Tolo News channel reported that 43 security personnel have been killed and wounded and 17 others were taken hostage by the militant group during the battle.
"Ghazni City remains under Afghan government control", Lt. Col. Martin O'Donnell, a spokesman for Operation Resolute Support and U.S. Forces Afghanistan, told Military.com on Tuesday.
Some bodies had been double-counted when they were being taken to hospital from the blast site following Wednesday's attack, the ministry said on Thursday.
The Taliban have not claimed a major assault in Kabul for weeks.
Afghan forces appeared to have finally pushed Taliban fighters from the strategic city of Ghazni on Wednesday, as shopkeepers and residents warily returned to the streets after days of intense ground fighting and USA airstrikes.
The Taliban issued a statement denying it was involved.
"If the U.S. continues to pursue the same strategy, advocated by the generals... then Taliban would just make more advances in Afghanistan", Rizk warned. The wounded were still arriving at the city's only hospital, which has been overwhelmed by casualties, he added. Afghan forces repelled the initial assault and in recent days have struggled to flush the insurgents out of residential areas where they are holed up.
Afghan security forces are fighting both the Taliban and ISIS in the country, with much of the emphasis in the east of the country.
Afghanistan is littered with unexploded ordnance left by decades of war.
On Tuesday night, two Afghan military outposts were attacked, in which at least 46 security officials were killed. He said seven attackers were killed and five were wounded during the battle, in which the Taliban used artillery and heavy weapons.