Taliban fighters have surrounded the city of Ghazni in central Afghanistan, taking over civilians' homes to fight security forces, officials said on Monday, the latest urban centre under threat from the insurgents.

The offensive was the latest on a provincial capital as the Taliban make a fresh push to surround cities and gain territory, emboldened by the departure of foreign forces.

"The situation in Ghazni city is very critical ... the Taliban use civilian houses as hideouts and fire upon the ANDSF (Afghan security forces), this makes the situation very difficult for the ANDSF to operate against the Taliban," said Hassan Rezayi, a member of Ghazni's provincial council.

Violence has surged in the country since US President Joe Biden announced in April that American troops would withdraw by Sept 11, ending 20 years in Afghanistan.

The US general leading the war in Afghanistan, Austin Miller, is to relinquish command on Monday, in a symbolic end to America's longest conflict.

Peace talks between the Taliban and the government have nominally been continuing in Qatar's capital but officials say they are making little progress.

Clashes between the two sides are also continuing in the southern province of Kandahar where the Taliban traditionally have had a strong presence, locals said. Ghazni is on the main road between Kabul and Kandahar city.

"Since the past four days, armed Taliban are attacking ... Kandahar city from the western direction," said Hamidzai Lalay, a former member of parliament who is fighting with armed men against the Taliban in Kandahar. "Afghan security forces, including special forces, are fighting the Taliban and trying to push them back."

Fawad Aman, a spokesman for the Ministry of Defence said the situation in Kandahar was "completely under control of ANDSF" which had carried out air and ground operations in recent days.

So far, the Taliban have not been able to hold provincial capitals but they have put pressure on Afghan security forces to respond to offensives around the country.

On Sunday, security forces, with the help of air strikes, repelled an assault by Taliban fighters on Taluqan, the provincial centre of a key northern province bordering Tajikistan.

Last week, Taliban fighters entered the capital of the western province of Badghis, seizing police and security facilities and attempting to take over the governor's office before special forces pushed them back.