The fall of Mazar-e-Sharif, the country's fourth-largest city, which Afghan forces and two powerful former warlords had pledged to defend, hands the insurgents control over all of northern Afghanistan, confining the Western-backed government to the centre and east.
And early on Sunday, an Aghan politician and the Taliban said the group had captured Jalalabad, cutting off Kabul from the east.
The United States and the UK are now rushing several thousand troops back into the country to evacuate citizens amid concern Kabul could soon be overrun.
Security forces from Mazar-e-Sharif were escaping towards the border, according to Afzal Hadid, head of the Balkh provincial council.
"The Taliban have taken control of Mazar-e-Sharif," he said. "All security forces have left Mazar city."
The city appeared to have fallen largely without a fight, although sporadic clashes continued nearby, he added.
Earlier in the day, the rebels seized a town south of Kabul that is one of the gateways to the capital.
Many Afghans have fled from the provinces to the capital, driven out by fighting and fearful of a return to hardline Islamist rule, as resistance from Afghan government forces crumbles.
As night fell on Saturday, hundreds of people were huddled in tents or in the open in the city, by roadsides or in car parks, according to one resident.
"You can see the fear in their faces," he said.
President Ashraf Ghani held urgent talks with local leaders and international partners but gave no sign of responding to a Taliban demand that he resign as a condition for any ceasefire.
His focus was "on preventing further instability, violence, and displacement of my people", he said in a brief televised address, adding that security and defence forces were being consolidated.
Qatar, which has been hosting so-far inconclusive peace talks between the Afghan government and the Taliban, said it had urged the insurgents to cease fire during a meeting with their representatives on Saturday.
Earlier the Taliban, facing little resistance, took Pul-e-Alam, capital of Logar province and 70 km (40 miles) south of Kabul, according to a local provincial council member, who spoke on condition of anonymity.
Police officials however denied reports the Taliban had advanced closer to Kabul from Pul-e-Alam, which is a staging post for a potential assault on the capital.
The town's capture came a day after the insurgents took the country's second- and third-biggest cities. The Taliban says it is close to capturing Maidan Shahr, another town close to Kabul.
An Afghan government official confirmed on Friday that Kandahar, the biggest city in the south and the heartland of the Taliban, was under the militants' control as US-led forces complete their withdrawal after 20 years of war.
The US-led invasion, which ousted the Taliban from power, was launched after the September 11 attacks on the United States in 2001.
Herat in the west, near the border with Iran, also fell to the group. The Taliban said on Saturday it had overrun the capitals of Kunar, Paktika and Paktia provinces on Afghanistan's eastern border, although this could not be immediately confirmed.
American troops have begun flying in to Kabul to help in the evacuation of embassy personnel and other civilians, a US official said on condition of anonymity.
The Pentagon has said two battalions of Marines and an infantry battalion will arrive in Kabul by Sunday evening, involving about 3,000 troops. An infantry brigade combat team will move to Kuwait to act as a quick reaction force for security in Kabul if needed.
Additional reporting by Reuters and AP
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