Taliban fighters captured the strategic Afghan city of Ghazni on Thursday, taking them to within 150km (90 miles) of Kabul following days of fierce clashes as the Islamist group ruled out sharing power with the government based there.

The Taliban captured Herat, Afghanistan’s third-largest city and a strategic provincial capital near Kabul, on Thursday.

Taliban fighters rushed past the Great Mosque in the historic city — which dates to 500 BC and was once a spoil of Alexander the Great — and seized government buildings. Witnesses described hearing sporadic gunfire at one government building while the rest of the city, which is near the border with Iran, fell silent under the insurgents’ control.

The speed and violence of the Taliban advance has sparked recriminations among many Afghans over US President Joe Biden’s decision to withdraw US troops and leave the Afghan government to fight alone.

The gateways to the capital have been choked with people fleeing violence elsewhere in the country this week, a western security source said. It was hard to tell whether Taliban fighters were also getting through, the source added.

With the last of the US-led international forces set to leave by the end of the month and end the US’s longest war, the Taliban are now in control of about two-thirds of the country. US intelligence suggests they could take the capital within 90 days.

Al Jazeera reported a government source saying it had offered the Taliban a share in power, as long as the violence comes to a halt.

Afghan government spokespeople were not immediately available for comment and it was not clear to what extent the reported power-sharing offer differed from terms already discussed at stalled talks in Qatar.

Taliban spokesperson Zabihullah Mujahid said he was unaware of any such offer but ruled out sharing power with a government whose authority the group did not acknowledge.

“We won’t accept any offer like this because we don’t want to be partner with the Kabul administration. We neither stay nor work for a single day with it,” he said.

Under a deal struck between the US and the Taliban last year, the insurgents agreed not to attack US-led foreign forces as they withdraw, in exchange for a promise not to let Afghanistan be used for international terrorism.

The Taliban also made a commitment to discuss peace. But intermittent talks with representatives of the US-backed government have made no progress, with the insurgents apparently intent on a military victory.

Ghazni, which lies 150km (95 miles) southwest of Kabul on the ancient route between the capital and the second city of Kandahar, was the ninth provincial capital the Taliban have seized in a week.

The militants on Thursday occupied Ghazni’s government agency headquarters after heavy clashes, a security official said.

“All local government officials, including the provincial governor, have been evacuated towards Kabul,” said the official who declined to be identified.

Fighting has also been intense in Kandahar. The city hospital had received scores of bodies of members of the armed forces and some wounded Taliban, a doctor said late on Wednesday.

Even when the Islamist group ruled the country from 1996-2001, it never controlled all of the north. This time, it appears to be determined to secure it fully before turning its attention to Kabul.

Finding rural districts too hard to defend, government forces have withdrawn to protect Kabul and other cities, prompting thousands of families to flee the provinces in hope of finding safety there.

The Taliban said they had seized airports outside the cities of Kunduz and Sheberghan in the north and Farah in the west, making it even more difficult to supply beleaguered government forces. They said they had also captured the provincial headquarters in Lashkar Gah, the capital of the southern province of Helmand, a hotbed of militant activity.

Government officials there were not immediately available for comment. Fighting had also flared in the northwestern province of Badghis, its governor said.

Kandahar and other southern and eastern provinces bordering Pakistan have long been Taliban heartlands but it has been in the north where they have made their biggest gains in recent weeks.

President Ashraf Ghani flew to northern Mazar-i-Sharif on Wednesday to rally old warlords he had previously tried to sideline, now needing their support as the enemy closes in. In Washington, a US defence official on Wednesday cited US intelligence as saying the Taliban could isolate Kabul in 30 days and possibly take it over within 90.

Biden said on Tuesday he did not regret his decision to withdraw US forces and urged Afghan leaders to fight for their homeland.

The Taliban risk isolating the country if they do seize overall control.

“Attempts to monopolise power through violence, fear, and war will only lead to international isolation,” the charge d’affaires at the US embassy, Ross Wilson, said on Twitter.

German foreign minister Heiko Maas said Berlin would not provide financial support to Afghanistan if the Taliban take over and introduce sharia religious law. The violence has also raised concerns in Europe of more refugees arriving there. Germany, the Netherlands and Switzerland have said they would not, for now, deport Afghans seeking asylum.

The Taliban controlled most of Afghanistan before they were ousted in 2001 for harbouring Osama bin Laden. A new generation of Afghans, who have come of age since 2001, worry that the progress made in areas such as women’s rights.