The UK is seeking international agreement to ensure the Taliban sticks to its commitment to allow safe passage for Afghans and foreign nationals who want to leave Afghanistan.
A series of diplomatic meetings will be held this week with Foreign Secretary Dominic Raab set to hold talks with Turkish and Qatari officials.
It comes as troops arrived back in the UK after ending their Afghan operation.
The government says it will continue to help people eligible for resettlement.
While more than 15,000 people have been evacuated by the UK since 14 August, hundreds of people who are entitled to come to the country have been left behind.
It is feared that about 800 to 1,100 eligible Afghans, including those who worked for the UK government, and 100 to 150 British were unable to get on evacuation flights.
The Foreign Office says the UK and many other countries had been given assurances by the Taliban that foreign nationals and Afghan citizens with proper documentation will be allowed to leave the country.
Even if the Taliban is true to its word there is still uncertainty for those who are able to get to its borders as processing centres have yet to be set up in neighbouring countries.
A meeting of the ambassadors from the five permanent members of the UN Security Council – the US, France, China, Russia and the UK – will also take place.
