American helicopters and drones were deployed to help push the Taliban back, the BBC reported, with multiple homes and government buildings reportedly destroyed by the fighting. "Morale is sinking. There aren't enough soldiers and police in the city right now to resist", Mr. Faqiri said.
The fighting on Sunday came after claims by the Afghan government that it had made significant gains against the insurgents.
"The Afghan peace process, withdrawal of foreign forces from Afghanistan, and restoration of peace were also brought under discussion", the Taliban statement said.
Interior ministry spokesman Najib Danish said fresh reinforcements had arrived in the area and were battling Taliban fighters north of Ghazni, and that the insurgents were in no position to take control of the city.
Mr. Danish said at least 25 security forces had died in the fighting along with 150 Taliban fighters.
Top security and government officials, including the military chief of staff, were now in Ghazni, leading the "clearing-up operations" in different parts of the city, Barmak said.
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"What wouldn't be helpful would be if the Uzbek efforts to facilitate lines of communication with the Taliban are not closely coordinated with the Afghan government", he said.
Many telecoms masts were destroyed during heavy fighting on Friday, making it hard to establish contact with the city, some two hours drive south of the capital Kabul, and there were conflicting accounts from government and Taliban spokesmen. The highway from Kabul to Afghanistan's southern provinces, which runs through Ghazni, is still closed.
In May, the Taliban attacked the western city of Farah.
A senior official, who spoke on condition of anonymity because he was not authorised to speak to the media, said around 80 members of the security forces, as well as an unknown number of civilians had been killed.
Islamic State also claimed responsibility for a recent blast in the country, with 29 people dead and 81 injured following, south of Kabul, two days ago.
The Taliban conducted an all-out assault on Ghazni, the capital of the Ghazni province on Friday.
U.S. Army Lieutenant Colonel Martin O'Donnell, a spokesman for the U.S. -led military coalition in Afghanistan, told reporters that initial reports suggested "minimal" casualties among Afghan forces.
But Thursday's assault comes ahead of a possible ceasefire announcement to coincide with the holiday of Eid-al Adha later this month.
Still, Andrew Wilder, vice president of Asia programs at the U.S. Institute of Peace said Washington would welcome a "constructive" Russian role in finding a way toward a peace pact in Afghanistan.