Officials have said Ghazni, a strategic provincial capital two hours from Kabul, remains in government hands and that security forces are conducting a clearing operation.
But residents told AFP the insurgents remained in the streets, burning buildings and targeting civilians.
The United Nations said unverified reports put civilian casualties at more than 100 since the Taliban entered the city late Thursday, with residents also at risk from several days of US airstrikes.
An MP from Ghazni, Shah Gul Rezaye, said Tuesday that some parts of the city had been cleared.
But in others "the Taliban have positioned their fighters in high buildings shooting at security forces from there," he added.
Communication networks remained largely down, making any information difficult to verify.
"Ghazni is a ghost city now. The Taliban are going from house to house to find government officials or their relatives to kill," said one resident, Sayed Zia.
"Those who can are fleeing."
Afghan special forces sent to bolster threatened city defenses
Another resident also said the Taliban were killing civilians who refused to help them.
"I saw two trucks full of coffins going toward a cemetery in the city. They all seemed to be civilians," said Abdullah, who asked to only use one name.
"The city is full of smoke. Everywhere they go they set the places on fire," he said, adding that shops were being looted, with water and food scarce.
Other residents have told AFP of bodies littering the streets of the city in recent days.
"So far the fighting has reportedly resulted in 110 to 150 civilian casualties. The numbers still need to be verified," said a report by the UN Office for the Coordination of Humanitarian Affairs.
Afghan Taliban delegation visits Uzbekistan to discuss peace, security
Clearing operations in urban centres are inherently dangerous and slow. Reports the Taliban are hiding in residents' homes and marketplaces "heightened the risk of civilian casualties arising from any military aerial response," the UN warned.
Bombs placed along the road leading north and south from the city also "prevented civilians from safely fleeing the violence", it said.
On Monday the Afghan defence minister said at least 100 security forces had been killed in the fighting so far, and "20-30" civilians.
Ghazni lies along the major Kabul-Kandahar highway, effectively serving as a gateway between Kabul and the militant strongholds in the south.
Taliban militants overrun Afghan army base, capture dozens of soldiers
The assault on the city has been the largest tactical onslaught by the Taliban since an unprecedented truce in June brought fighting between security forces and the Taliban to a temporary halt, providing war-weary Afghans some welcome relief.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ