Jawad Mujadidi, a provincial council member from Badakhshan, said the Taliban had laid siege to Faizabad before launching an offensive on Tuesday.
â€œWith the fall of Faizabad, the whole of the north-east has come under Taliban control,â€ Mujadidi said.
The Taliban want to defeat the US-backed government and reimpose strict Islamic law. The speed of their advance has shocked the government and its allies.
Biden urges leaders to fight
US President Joe Biden urged Afghan leaders to fight for their homeland, saying on Tuesday he did not regret his decision to withdraw. He said Washington had spent more than $US1 trillion over 20 years and lost thousands of US troops.
The United States was providing significant air support, food, equipment and salaries to Afghan forces, he said.
White House press secretary Jen Psaki declined to comment on Wednesday about assessments that Kabul could soon be overtaken by the Taliban. â€œWe are closely watching the deteriorating security conditions in parts of the country, but no particular outcome, in our view, is inevitable,â€ she said.
The United States will complete the withdrawal of its forces this month in exchange for Taliban promises to prevent Afghanistan being used for international terrorism. Psaki said the timeline holds and reiterated the administrationâ€™s view that Afghan forces have the US support they need to fight back.
The Afghans â€œneed to determine … if they have the political will to fight back and if they have the ability to unite as leaders to fight back,â€ she said.
The Taliban promised not to attack foreign forces as they withdraw but did not agree to a ceasefire with the government. A Taliban commitment to talk peace with the government side has come to nothing.
A senior Taliban leader said the head of the groupâ€™s political office, Mullah Abdul Ghani Baradar, met US Special Envoy for Afghan Reconciliation Ambassador Zalmay Khalilzad in Doha on Tuesday. No details of the meeting have been released.
The Troika Plus â€“ a platform led by the United States, China and Russia â€“ was expected to meet on Wednesday. The Taliban leader, requesting anonymity, said a Taliban delegation would take part.
The Taliban advances have raised fears of a return to power of the hardline militants who emerged in the early 1990s from the chaos of civil war. They controlled most of Afghanistan from 1996 to 2001, when they were ousted by a US-led campaign for harbouring al-Qaeda chief Osama bin Laden.
A new generation of Afghans, who have come of age since 2001, fears the progress made in areas such as womenâ€™s rights and media freedom will be squandered.
Afghan officials have appealed for pressure on Pakistan to stop Taliban reinforcements and supplies flowing over the border. Pakistan denies backing the Taliban.
During their previous rule, the Taliban never completely controlled the north. Now they seem intent on securing it before closing in Kabul.
Ghani is appealing for help from the regional warlords he spent years sidelining as he tried to project the authority of his central government over wayward provinces.
In the south, government forces battled Taliban fighters around the city of Kandahar and thousands of civilians from outlying areas had taken refuge there, a resident said. A doctor there said scores of bodies of Afghan forces have been received, and some wounded Taliban fighters have sought medical support.
The Taliban have captured districts bordering Tajikistan, Uzbekistan, Iran, Pakistan and China, heightening regional security concerns.
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