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The collapse of Jalalabad, near a major border crossing with Pakistan, leaves Afghanistan’s central government in control of only Kabul and seven of the country's 34 provincial capitals.
In a nationwide offensive, the Taliban have defeated, co-opted or sent Afghan security forces fleeing from large parts of the country, even with the country's military receiving air support from the US military.
Afghan President Ashraf Ghani, who spoke to the nation on Saturday for the first time since the offensive began, appears to be increasingly isolated as well.
Militia leaders he negotiated with days earlier have surrendered to the Taliban or fled, leaving Mr Ghani without a military option. Negotiations in Qatar, where the Taliban have a political office, have also failed to stop the insurgents’ advance.
Last week, a US intelligence source said Kabul could hold out for at least three months.
It followed the Taliban's seizure of the northern city of Mazar-i-Sharif late on Saturday, which also fell with little fighting.
"There are no clashes taking place right now in Jalalabad because the governor has surrendered to the Taliban," an Afghan official in Jalalabad told Reuters.
"Allowing passage to the Taliban was the only way to save civilian lives."
Another security official in the city said the Taliban had agreed to give safe passage to government officials and security forces departing the city.
The decision to surrender was taken to avoid "casualties and destruction", the official said.
After US-led forces withdrew the bulk of their remaining troops in the past month, the Taliban campaign accelerated as the Afghan military's defences appeared to collapse.
On Saturday, US President Joe Biden authorised the assignment of 5,000 troops to help move US citizens to safety and ensure an "orderly and safe" withdrawal of American military personnel.
A US defence official said that number included 1,000 newly approved troops from the 82nd Airborne Division.
Taliban fighters entered Mazar-i-Sharif on Saturday virtually unopposed as security forces escaped along the road to neighbouring Uzbekistan, about 80 kilometres to the north, provincial officials said.
Unverified video on social media showed Afghan military vehicles and men in uniforms crowding the iron bridge between the Afghan town of Hairatan and Uzbekistan.
Two influential militia leaders supporting the government – Atta Mohammad Noor and Abdul Rashid Dostum – also fled. Mr Noor said on social media that the Taliban had been handed control of Balkh province, where Mazar-i-Sharif is located, due to a "conspiracy".
Late on Saturday, the Taliban said their rapid gains showed they were popularly accepted by the Afghan people and reassured both Afghans and foreigners that they would be safe.
The Taliban "will, as always, protect their life, property and honour and create a peaceful and secure environment for its beloved nation", the insurgents said.
Diplomats and aid workers will also not face any problems, they said.
Early on Sunday, refugees from Taliban-controlled provinces were seen unloading belongings from taxis in Kabul, families stood outside embassy gates, while the city centre was packed with people stocking up on supplies.
Hundreds of people slept huddled in tents or in the open in the city, by roadsides or in car parks, a resident said on Saturday night.
"You can see the fear in their faces," he said.
Western governments were accelerating plans to remove their embassy staff, citizens and Afghans who had worked for them.
The US State Department has reached out to advocates to request names of Afghans in Kabul who have worked with the Americans and need to be moved to safety, two sources said.
The list of names could include journalists and human rights activists.
The UK ambassador will leave the country by Sunday evening, UK media reported.
The country, which was sending 600 troops, sped up the departure of its citizens owing to the rising risk that the Taliban would overrun the airport, UK media reported.
Mr Biden said his administration told Taliban officials in Qatar that any action that put US personnel at risk "will be met with a swift and strong US military response".