The head of Nato vowed to "stay vigilant" on Thursday to ensure Afghanistan does not become a safe haven for international terrorists.
Secretary General Jens Stoltenberg said he expects the Taliban to "live up to their commitment" not to host terrorists.
Mr Stoltenberg admitted that the Taliban's swift takeover of Afghanistan had not been anticipated by Nato and had taken his organisation by surprise.
The comments came as the secretary general said he would chair an extraordinary meeting of foreign affairs ministers on Friday to address the crisis.
"We need to remember we went in [to Afghanistan] to fight international terrorism and for 20 years we have prevented Afghanistan from being a safe haven for international terrorists and we have been able to degrade Al Qaeda," he said.
"We expect the new rulers in Kabul to live up to their commitment not to host international terrorists in Afghanistan and we will stay vigilant."
He said Nato now faces "difficult questions" over the collapse after years of investment in Afghan security services, but maintains it is still a "strong alliance".
"There are difficult lessons to be learnt for Nato," he said.
"Despite all the money and training and equipment we provided to Afghanistan security forces we saw the political and military leadership collapse. It raises difficult questions for Nato to look into."
The EU's Josep Borrell told the European Parliament on Thursday that his major concerns included a possible surge in refugee numbers and increasing complexity in Central Asia – with Turkey, China and Russia all vying to increase their influence in the region.
Mr Borrell said the EU was being forced to "establish channels of communication" with the Taliban to ensure safe exits for its nationals and Afghan staff and their families.
"Yes, we have to talk with the Taliban but that doesn't mean recognition," he said.
Ben Wallace, the UK defence secretary said Britain was preparing for an Al Qaeda resurgence.
"Al Qaeda will look at this as an opportunity," he said. "We will have to gear up, tool up and we already have the capabilities to deal with some of that."
The UK says up to 10 Royal Air Force flights a day are departing to fly out hundreds of people.
The Taliban said it will allow safe passage to Kabul’s airport, but there are concerns that some Afghans are too scared to leave their homes and attempt the journey.
Chaotic scenes erupted at Kabul airport as thousands tried to flee and on Thursday it was reported that at least 12 people had been killed in the area.