Germany said evacuation flights had begun and Chancellor Angela Merkel told her party that up to 10,000 people may need to be rescued, including 2500 Afghan support staff, human rights activists and lawyers.
Britainâ€™s ambassador remained at the airport processing visas as pressure mounted in the UK for the government to urgently facilitate safe passage for interpreters and others who had assisted the allied military mission.
The UKâ€™s Defence Secretary Ben Wallace broke down as he admitted that â€œsome people wonâ€™t get backâ€.
â€œItâ€™s a really deep part of regret for me … some people wonâ€™t get back,â€ he told radio station LBC.
â€œSome people wonâ€™t get back and we will have to do our best in third countries to process those people.â€
Asked why he felt the situation â€œso personally,â€ Mr Wallace said: â€œBecause Iâ€™m a soldier.â€
â€œBecause itâ€™s sad and the West has done what itâ€™s done, we have to do our very best to get people out and stand by our obligations and 20 years of sacrifice is what it is,â€ he said.
Meanwhile, neighbouring Uzbekistan said it had shot down an Afghan military jet that violated its airspace on Sunday night, but did not say how many people were on board and if there were any survivors.
The jet crashed in Uzbekistanâ€™s southernmost Surxondaryo province adjacent to Afghanistan.
â€œUzbekistanâ€™s air defence forces prevented an attempt by an Afghan military aircraft to illegally cross Uzbekistanâ€™s border,â€ Bahrom Zulfikorov, a spokesman for Uzbekistanâ€™s defence ministry, said.
On Sunday, the Afghanistan President Ashraf Ghani fled the country, abruptly ending the Western-backed government, signalling a triumphant return of the Taliban who were ousted from the capital two decades ago, when the US began its longest-ever war after the September 11 attacks.
The US-trained Afghan army barely put up a fight as the Taliban advanced across the country in just over a week, culminating in the seizure of the capital, in a mostly peaceful manner, on Sunday.
Taliban fighters entered the city after Ghani fled, having been instructed to wait outside the city until the government had surrendered.
On Monday, they began collecting weapons from civilians, with a Taliban official saying citizens no longer needed them for their own personal protection.
â€œWe understand people kept weapons for personal safety. They can now feel safe. We are not here to harm innocent civilians,â€ the official told Reuters.
Kabul resident Saad Mohseni, director of the MOBY group media company, said Taliban soldiers had come to his company compound to collect government issued weapons.
There were scattered reports of looting and armed men knocking on doors and gates, and there was less traffic than usual on eerily quiet streets. Fighters could be seen searching vehicles at one of the cityâ€™s main squares.