US officials said more than 4,000 Americans were among those flown out of Hamid Karzai International Airport in the Afghan capital.
Several thousand other people have been evacuated by allied European nations, such as Germany and the United Kingdom.
The Taliban urged skilled Afghans not to flee the country on Tuesday and warned the United States and its NATO allies they would not accept an extension to the evacuation deadline.
A spokesman for the hardline Islamist group told America to stop taking “Afghan experts,” such as engineers and doctors, out of the country. “This country needs their expertise. They should not be taken to other countries,” Taliban spokesman Zabihullah Mujahid told a press conference in the capital.
European nations have said they would not be able to airlift all at-risk Afghans before the August 31 cut-off, and Biden has faced calls from all corners to extend the evacuation window.
Mujahid said the Islamist group opposes an extension. “They have planes, they have the airport, they should get their citizens and contractors out of here,” he said.
Germany said Tuesday Western allies simply cannot fly out every Afghan who needs protection before the cut-off date. “Even if (the evacuation) goes on until August 31 or even a few days longer, it will not be enough,” Foreign Minister Heiko Maas told Bild TV.
France said it would have to end evacuations from Kabul’s airport on Thursday if the United States stuck to the deadline, and Spain said it would not be able to rescue all Afghans who served Spanish missions.
Spanish Defence Minister Margarita Robles said Taliban checkpoints and violence were making it difficult for people to reach Kabul airport to catch one of Spain’s daily military flights out of Afghanistan.
EU leaders at the G7 meeting urged Biden to continue to secure Kabul airport until operations to evacuate vulnerable Afghans are complete. Many Afghans fear a repeat of the brutal interpretation of Islamic law that the Taliban implemented when first in power from 1996-2001, or retribution for working with the US-backed government over the past two decades.
On Tuesday, Mujahid said female Afghan government workers should stay home until security conditions in the country improve.
Meanwhile, the World Bank said it has suspended aid to Afghanistan and was “deeply concerned” about the situation there after the Taliban seized power, especially for the prospects of women.
“We have paused disbursements in our operations in Afghanistan and we are closely monitoring and assessing the situation,” a World Bank official said.
The World Bank has more than two dozen development projects ongoing in the country and has provided $5.3 billion since 2002, mostly in grants, according to the bank’s website.
The Taliban achieved their stunning victory after Biden pulled out nearly all American troops from Afghanistan, following through on a deal struck with the movement by former president Donald Trump.
However, Biden was forced to redeploy thousands of troops after the fall of Kabul to oversee the airlift.
According to The Washington Post, US Central Intelligence Agency chief William Burns held a secret meeting in Kabul on Monday with Taliban co-founder Mullah Abdul Ghani Baradar, although no details were reported and neither the CIA nor the Taliban confirmed it.
The rush to leave Kabul has sparked harrowing scenes and left at least eight people dead. The Taliban have repeatedly claimed to be different from their 1990s incarnation, and have declared an amnesty for government forces and officials.
But an intelligence assessment conducted for the United Nations said militants were going door-to-door hunting former government officials and those who worked with US and NATO forces.