Downing Street said ministers and senior officials would meet on Sunday afternoon to discuss the worsening situation.
Earlier No 10 sources said that the Prime Minister would seek a recall of Parliament this week after insurgents entered the outskirts of Kabul.
It came as Britain and other western countries were scrambling to get their remaining nationals out before it was too late.
The lead elements of a 600-strong UK force – including Paras from 16 Air Assault Brigade – were understood to be in the capital to assist with the operation.
The Foreign, Commonwealth and Development Office said the ambassador, Sir Laurie Bristow, remained in Kabul, although the UK diplomatic presence had been reduced.
“We are doing all we can to enable remaining British nationals who want to leave Afghanistan to do so,” a spokesman said.
At the same time officials said they were doing all they could to assist the estimated 2,000 Afghans who had worked with the British during their time in the country to relocate while there was still time.
The Home Office said in a statement posted on Twitter that it had already relocated over 3,300 Afghan staff and their families, adding : “We will continue to fulfil our international obligations and moral commitments.”
The Commons authorities said Speaker Sir Lindsay Hoyle had agreed to a recall, with MPs returning to Westminster on Wednesday while the Lords will also return.
Among senior parliamentarians there was shock and anger at the speed of the Afghan collapse after the West had invested billions in building up the country’s armed forces.
Many cities fell to the Taliban without a fight after tribal elders stepped in to negotiate the withdrawal of government forces in order to avoid bloodshed.
The chairman of the Commons Foreign Affairs Committee, Tom Tugendhat, said it was “the biggest single foreign policy disaster since Suez”, while Defence Committee chairman Tobias Ellwood said it was a humiliation for the West.
Labour leader Sir Keir Starmer said ministers needed to explain what they intended to do to avert a looming humanitarian crisis and prevent Afghanistan again becoming a base for international terrorism.
“The situation in Afghanistan is deeply shocking and seems to be worsening by the hour,” he said.
“The immediate priority now must be to get all British personnel and support staff safely out of Kabul. The Government has been silent while Afghanistan collapses which, let’s be clear, will have ramifications for us here in the UK.”
The Taliban insisted that there would be no reprisals against Afghans who had worked for the government or for foreign countries and that they were seeking a peaceful transfer of power.
However, such assurances were greeted with scepticism by Mr Tugendhat who said the priority had to be to get as many people as possible out of Kabul.
“This isn’t just about interpreters or guards. This is about those people who we trained in special forces to serve alongside us, those who helped us to understand the territory through our agencies and our diplomats,” he told BBC News.
“This is the people who, on our encouragement, set up schools for girls. These people are all at risk now.
“The real danger is that we are going to see every female MP murdered, we are going to see ministers strung up on street lamps.”
Despite the decision of the Biden administration to withdraw the remaining US troops which triggered the collapse, Mr Ellwood said it was still not too late to turn the situation around.
He called for the despatch of the Royal Navy carrier strike group to the region and urged the Prime Minister to convene an emergency conference of “like-minded nations” to see what could be done.
“I plead with the Prime Minister to think again. We have an ever-shrinking window of opportunity to recognise where this country is going as a failed state,” he told Times Radio.
“We can turn this around but it requires political will and courage. This is our moment to step forward.
“We could prevent this, otherwise history will judge us very, very harshly in not stepping in when we could do and allowing the state to fail.”