His words were echoed by Gen Yafti, who told reporters: "Strategic locations and centres in the city are under the control of Afghan forces and the Taliban are hiding inside people's homes and shops and resisting".
Government officials say that all key government buildings are still under government control, including the governor's compound, and the NDS and Police headquarters.
Taliban control of the city would not only cut off northern Afghanistan and the capital from the traditional Taliban homelands in the south, it would also prove a severe defeat for the USA and Afghan strategy of holding population centers rather than territory.
Clashes broke out when hundreds of Taliban fighters stormed Ghazni city in the early hours of Friday morning.
Afghanistan's Army Chief of Staff Mohammad Sharif Yaftali could travel to Ghazni province on Sunday in order to take control of the ongoing battle, military officials said.
Defense Ministry spokesman Mohammad Radmanesh told RFE/RL's Radio Free Afghanistan that Ghazni, some 150 kilometers southeast of Kabul, was under complete control of the security forces.But he saidclearance operations were continuing.
A Taliban spokesman confirmed its officials from the Qatar-based political office concluded a four-day visit to Uzbekistan on Friday, where it held talks with the foreign minister and the Uzbek presidential envoy for Afghanistan.
Unconfirmed reports said both sides suffered heavy casualties, with Aghanistan's 1TV reporting more than 90 government forces had been killed along with 13 civilians, and more than 100 wounded.
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.
A spokesman for USA forces in Afghanistan also described the fight for Ghazni as a clearance operation, with sporadic clashes between security forces and insurgents punctuating relative calm. The Wall Street Journal's Ehsanullah Amiri said that 15 hours after the attack began, the city still hadn't been cleared of Taliban fighters.
The US said that the city remained under government control.
It had supplied body bags to the provincial hospital and was ready to provide more assistance.
The assault was a major show of force by the Taliban, who had infiltrated deep into the city and attacked from several directions. But details of the fighting were unclear as most of the city's telecoms masts were destroyed in fighting over recent days. The government had been considering a ceasefire for the upcoming Eid al Adha holiday, similar to a truce in June over the Eid al Fitr holiday.
"Fear is spreading in Ghazni as the day ends, the Taliban might intensify their attack as it gets dark".
"We stand ready to create all necessary conditions, at any stage of the peace process, to arrange direct talks between the government of Afghanistan and Taliban movement", Mirziyoyev told an global peace conference in the Uzbek capital in March.