The militant group takes the eastern city of Jalalabad without a fight as it closes in on the capital.
Tensions are rising in the Afghan capital, Kabul, as the Taliban continue their rapid advance towards the city.
The militants seized the eastern city of Jalalabad early on Sunday, leaving Kabul as the only major city still under government control.
It followed the capture on Saturday of the government’s northern bastion of Mazar-i-Sharif.
The collapse of government forces has left President Ashraf Ghani under growing pressure to resign.
He faces a stark choice between surrender or a fight to hold the capital.
Meanwhile, the US said it was deploying 5,000 troops to help evacuate its nationals from the beleaguered country.
President Joe Biden has defended his decision to escalate the US withdrawal from Afghanistan, saying he could not justify an “endless American presence in the middle of another country’s civil conflict”.
Reports on Sunday morning said the Taliban took control of the city without a shot being fired.
“There are no clashes taking place right now in Jalalabad because the governor has surrendered to the Taliban,” an Afghan official based in the city told Reuters news agency.
“Allowing passage to the Taliban was the only way to save civilian lives.”
The capture of Jalalabad means the Taliban have secured the roads connecting the country with Pakistan.
It came hours after Mazar-i-Sharif – the capital of Balkh province and fourth-largest city in Afghanistan – also fell largely without a fight.
Abas Ebrahimzada, a lawmaker from Balkh, told the Associated Press news agency that the national army were the first to surrender, which then prompted pro-government forces and other militia to give up.
The insurgents now control 23 of 34 provincial capitals.