The Afghan Military says the armed forces have foiled Taliban's bid to carry out coordinated attack on security outposts in Sarobi district of Kabul.
News of what exactly is happening in Ghazni, a provincial capital on the key road between Kabul and Kandahar, is hard to get after the militants damaged a telecommunications tower.
Mohammad Sharif Yaftali, Afghan army chief of staff, said on Sunday the city was not under threat of collapse and heavy fighting was under way to push back the Taliban from city limits.
The insurgents entered the southeastern city of Ghazni overnight, reportedly hiding inside homes before launching the brazen attack in the early morning hours.
Some sources said some shops were open in the central parts of Ghazni City and that the clashes are ongoing in western parts of the city.
Taliban spokesman Zabihullah Mujahid has claimed in a social media post that the group has captured Ghazni's prison and that prisoners have been freed.
The onslaught was the latest attempt by the Taliban to overrun an urban centre and comes as pressure increases on the insurgents to begin peace talks with the government to end the almost 17-year-old war. Local television station 1TV says the number of fatalities has risen to more than 100, but there is no official confirmation.
The anti-government armed militant groups including Taliban militants have not commented regarding the report so far.
Hamidullah Nowroz, member of Ghazni Provincial Council told TOLOnews on Saturday that Taliban militants were planning to attack and overrun Ghazni City months ago. One lawmaker said that only the governor's office, the police headquarters and the intelligence police facility remained in government hands.
The Red Cross said in a message on Twitter that it was watching the situation closely.
While little firsthand information was available from the city Sunday and most cellphone communication was cut off, social media showed videos of badly burned and damaged buildings.
There are also reports the road outside the city has been mined, making it hard for residents to escape.
"It is over and the city is taken", said a man standing outside his home, with several Taliban insurgents nearby.
Abdul Wakil, who had managed to flee, told Reuters: "There was burning and fire and dead bodies everywhere in the city".
A US military spokesman said Sunday that American aircraft had conducted five airstrikes on Saturday and 10 on Sunday.
The Taliban have not taken a major provincial centre since they overran the northern city of Kunduz in 2015 and the assault on Ghazni was a major blow to the Western-backed government just weeks before parliamentary elections scheduled for October 20.