Mobile services in the city remained down after militants damaged a telecommunication tower and targeted several media offices in Ghazni, making information hard to verify.
An army official in Kabul, Sharif Yaftali, told journalists Sunday that "strategic and key areas" of Ghazni are under control of the government but that insurgents had taken cover in populated areas, slowing efforts to drive them out.
The descriptions stood in stark contrast to statements given by Afghan and United States' officials on Saturday, who said government forces were firmly in control of the city and vowed that Ghazni was in no danger of being seized by the Taliban.
He said officials hope to restore security and reopen the highway within two days.
"In Ghazni, only the police headquarters, governor's office and a few departments are under Afghan forces' control, the rest are under the Taliban fighters' control", he added.
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.
The Taliban launched the assault in the early hours of Friday. Both were retaken by government forces after heavy fighting, but the near-takeovers by the Taliban gave the insurgent group a psychological boost.
There were no confirmed reports on casualty numbers, but one Afghan TV channel quoted hospital officials as saying that more than 90 members of the security forces and 13 civilians had been killed, as well as an unknown number of Taliban fighters.
Security officials said that due to clashes in parts of Sayed Abad district in Wardak province, the Kabul-Kandahar highway is still close to traffic.
President Ashraf Ghani made no mention of the crisis during an extended speech on youth affairs on Sunday and with little coming out from the government, people were left to rely on alternative sources of information.
There are also reports the road outside the city has been mined, making it hard for residents to escape.
"There was burning and fire and dead bodies everywhere in the city", said Abdul Wakil, a local resident who escaped, told Reuters at a checkpoint into Kabul.
"It is over and the city is taken", said a man standing outside his home, with several Taliban fighters nearby.
USA military headquarters in Kabul said sporadic clashes were occurring and American aircraft had conducted five strikes on Saturday and four more on Sunday.
On Sunday, Lt Col Martin O'Donnell, US Forces Afghanistan spokesperson, said the Afghan army "continue to hold their ground and maintain control of all government centres".