The White House made the announcement on Saturday soon after it was announced that insurgents had captured Mazar-e-Sharif, the Afghan government’s last northern stronghold as city after city has toppled.
The US and the UK are now rushing troops back into the country to evacuate citizens amid concern that Kabul could fall.
Mr Biden said the troop deployment was “to make sure we can have an orderly and safe drawdown of US personnel and other allied personnel and an orderly and safe evacuation of Afghans who helped our troops during our mission and those at special risk from the Taliban advance”.
Mr Biden went on to say that he had ordered US military and intelligence forces “to ensure that we will maintain the capability and the vigilance to address future terrorist threats from Afghanistan”
He also underlined the US message to the Taliban that any ground action that “puts US personnel or our mission at risk: would be met by a “swift and strong” military response.
The president also placed Ambassador Tracey Jacobson, head of the administration’s Afghanistan task force, in charge of Afghan special immigrant visa applicants and other Afghan allies.
“Our hearts go out to the brave Afghan men and women who are now at risk. We are working to evacuate thousands of those who helped our cause and their families,” the president stated.
The fall of Mazar-e-Sharif this weekend - which Afghan forces and two powerful former warlords had pledged to defend - is a strategic blow to the Western-backed government to the centre and east.
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.
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