The city's power remained cut, with food prices rising, they said.
Ghazni has been the scene of fierce fighting between the Taliban and Afghan security forces in the past four days.
"Ghazni City remains under Afghan government control, and the isolated and disparate Taliban forces remaining in the city do not pose a threat to its collapse as some have claimed", Lt. Col. Martin O'Donnell, a spokesman for USA forces in the country, told Military Times.
Trump also gave the USA military more leeway to attack the Taliban, and a few thousand additional US troops were sent to Afghanistan this year as part of an effort to improve the effectiveness of training and advising Afghan ground forces, while also developing a small Afghan air force. The top USA military commander in Afghanistan has denied that the United States is ready to negotiate directly with the Taliban, but the US government could participate in talks between the Taliban and the Afghan government.
A US military spokesman told NPR's Diaa Hadid that some 140 Taliban insurgents have also died - meaning the fighting has already cost almost 300 lives since the Taliban launched its assault.
Almost 100 soldiers and police officers have been killed, with many wounded according to reports from security officials, who also added that casualties on the Taliban side are similarly heavy.
There were claims that Ghazni's police headquarters had fallen. "The situation was very bad and all shops were closed", said Abdul Wakil, an eyewitness who fled from Ghazni.
It was also the largest tactical operation launched by the Taliban since an unprecedented truce in June brought fighting between security forces and the Taliban to a temporary pause, providing war-weary Afghans some welcome relief.
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He added: "This country will neither stop, nor bow nor get exhausted ". The OROP (one rank, one pension) demand was pending for decades.
U.S. and Afghan officials have said the prospects for peace talks are encouraging.
The Taliban have seized several districts across Afghanistan in recent years and stage near-daily attacks on Afghan security forces, but have been unable to capture and hold urban areas.
The United States and North Atlantic Treaty Organisation formally concluded their combat mission in Afghanistan at the end of 2014, but have since then repeatedly come to the aid of Afghan forces as they struggle to combat the resurgent Taliban.
The number of civilian casualties is not known but witnesses who have reached Kabul have reported seeing many bodies in the streets.
"The militants know our forces will not attack civilians so they are using young men as human shields to walk around the city and set buildings on fire", said one official in Kabul. Washington neither confirmed nor denied the meeting, but acknowledged Wells was in Qatar, where the Taliban maintain an office.
Afghan officials differed in their account, saying almost 200 Taliban fighters have been killed. "High profile talks by foreign governments with the Taliban that exclude the Afghan government risk providing too much legitimacy to the Taliban without getting much in return", Wilder said. These and other moves boosted the number of USA troops in Afghanistan by at least 3,500, to a total of more than 14,000.
There were quick assurances that the Taliban had been pushed back to the outskirts shortly after Friday.
Diplomats in Kabul said the government had admitted being taken by surprise by the attack and after days with minimal public comment from the presidential palace, Ghani announced on Twitter that reinforcements would be sent urgently.