Nearly 4,000 Afghan and British nationals have been evacuated from Afghanistan, but fears remain many could be left behind as the US prepares to leave the country.
Some 3,821 individuals have been rescued thanks to British efforts under Operation Pitting since 13 August, according to the Ministry of Defence, including 1,323 who have made it to the UK.
This includes embassy staff, British nationals and those eligible under the Afghan Relocation and Assistance Policy (ARAP) programme.
Nevertheless, fears are mounting that not all evacuees will make it out of the country before American forces leave the country on 31 August.
The MoD said the "priority" is to get all those eligible "out as swiftly and safely" as possible, in conjunction with the US, and as "long as the security situation allows".
However, Defence Secretary Ben Wallace has said "no nation will be able to get everyone out" of Afghanistan.
Writing for the Mail on Sunday, the cabinet minister said: "I have said all along that no nation will be able to get everyone out.
"It is a source of deep sadness for many of us across NATO, and no one wanted 20 years of sacrifice to end this way.
"We will do our best to the very last moment."
He added that the UK's efforts to help those left behind would continue after troops have left.
"We shall stand by our obligations and are investigating now how to process people from third countries and refugee camps," he said.
"We will establish a series of processing hubs across the region outside Afghanistan for those Afghans we have an obligation to bring to this country."
On Saturday, the US embassy in Afghanistan recommended US citizens avoid travelling to Kabul airport "because of potential security threats outside the gates" being linked to the so-called Islamic State.
But a Ministry of Defence spokeswoman stressed that neither UK flights nor processing were affected by the pause.
Time is running out ahead of the deadline set by US President Joe Biden, sparking fears Afghans who helped the West since 2001, and vulnerable women, will be left behind and at risk of recrimination from the Taliban.
Speaking on Friday, Mr Biden did not commit to extending the deadline, in a move that is likely to mean British troops must return home at the same time, as Kabul airport cannot be held without US enforcement.
Reports have suggested the last UK evacuation flight could be as soon as Tuesday, in order to give British troops enough time to leave safely.
Mr Biden and other international leaders face growing criticism amid the increasingly violent and desperate scenes outside Hamid Karzai International Airport, where thousands translators and other Afghan wartime helpers, along with their close family members, have gathered over the last week to seek evacuation.
The diplomat leading the UK's rescue mission in Afghanistan, Sir Laurie Bristow, said the Kabul airport evacuation effort is "without a doubt" his greatest international challenge.
In a statement issued by the Foreign Office, Sir Laurie, who is in Kabul, said: "The scale of this effort is enormous and is without a doubt the biggest international challenge I have worked on as a diplomat.
"Lives are at stake and I am incredibly proud of the tenacious efforts of my team during these challenging times, with military and civilian staff working together to successfully evacuate thousands of people in the last week."
The Pentagon said some 17,000 people have been evacuated by the US since 15 August, but Josep Borrell, the EU's foreign policy chief, told AFP news agency that it was "mathematically impossible" for the US to evacuate all Afghans with travel permits by the 31 August deadline.
On Saturday morning, Sky News' chief correspondent Stuart Ramsay, reporting from Kabul, witnessed people at the front of a crowd by the airport being "crushed to death", with British soldiers pulling those in danger to safety.
It was "the worst day by far" for violence and mayhem at the site, with at least three people believed to have been killed, as the security situation around the airport worsens.
On Saturday evening, Foreign Secretary Dominic Raab tweeted he had spoken with his US counterpart Antony Blinken and together they had pledged to "partner" on the evacuation process and to "forge an international strategy on counter-terror, humanitarian relief and regional stability".
Meanwhile, shadow foreign secretary Lisa Nandy shared a letter she wrote to Dominic Raab about the "crisis facing UK and Afghan nationals seeking evacuation from Afghanistan".
The senior Opposition figure said Labour MPs had been hearing of people being "shot at, beaten and raped" while they wait to be called forward at Kabul airport.
She asked Mr Raab whether NATO allies could put in place a "military policing operation" at the gates of the airport or within the internal processing zone.
Ms Nandy also requested that all MPs receive a briefing on the current state of affairs, complaining that Tory MPs had been given information when Opposition representatives had not.
At the same time, Boris Johnson and the United Nations secretary-general Antonio Guterres spoke and "agreed that... the international community must ensure the rights of women, girls and ethnic minorities are protected" in Afghanistan amid "the concerning situation on the ground", according to No 10.
According to Nato Secretary-General Jens Stoltenberg, several countries have requested that Kabul airport remain open for evacuations beyond 31 August to help get more people to safety.
Earlier, the Taliban's top political leader Mullah Abdul Ghani Baradar arrived in Kabul for talks on forming a new government.
A Taliban official said the new Taliban model of Afghan government may not be democracy by the same strict Western definition, but would protect everyone's rights.
Afghan officials familiar with talks held in the capital say the Taliban have said they will not make announcements on their government until the 31 August deadline for the troop withdrawal passes.
In its dialogue with a number of different officials and groups, the spokesman said it had been discussing how to ensure Western powers leave the country on amicable terms.
A senior official in the ousted government, Abdullah, tweeted that he and former president Hamid Karzai met with the Taliban's acting governor for Kabul on Saturday, who "assured us that he would do everything possible for the security of the people" of the city.