Foreign Secretary Dominic Raab has flown to Doha for talks with Qatari leaders on how to help British nationals and Afghans who are trying to leave Afghanistan.
The prospect of persuading the Taliban to reopen Kabul airport will be among the key issues discussed.
Mr Raab will also be briefed on talks between UK officials and the Taliban.
Qatar has become a key negotiator with the Taliban, which has had a political office in the country for eight years.
The Gulf state has already begun discussions about how best to ensure security at the airport.
At the start of his regional tour, Mr Raab will hold talks with the Emir of Qatar and the country's foreign minister.
British officials have been meeting with senior Taliban leaders in Doha and they will brief the foreign secretary on the outcome of those talks.
The Foreign Office said the British embassy to Afghanistan, which moved out of Kabul last week, was now up and running in Doha.
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Mr Raab's flight came hours after he was grilled by MPs on the Commons foreign affairs committee about the UK's withdrawal from Afghanistan.
The foreign secretary defended his handling of the crisis, saying the UK was "caught out" by the speed of the fall of Kabul to the Taliban, with intelligence at the time suggesting it would hold out until the end of the year.
But the committee's chairman, Conservative MP Tom Tugendhat, said a Foreign Office risk report from 22 July predicted a "very real danger of cities collapsing" after US forces withdrew.
The document, which was leaked to Mr Tugendhat and has been seen by BBC Two's Newsnight, warned the stalling of peace talks and the US withdrawal was leading to "rapid Taliban advances".
It said: "This could lead to: fall of cities, collapse of security forces. Taliban return to power, mass displacement and significant humanitarian need. The embassy may need to close if security deteriorates."
But the document does lend some credence to the foreign secretary's claim that he had not been warned of an imminent collapse of Kabul.
It talked of the UK "working with allies to ensure continued support for Afghan and security forces over the next 3-6 months on supporting the peace process".
The Foreign Office said it was a standard monthly report that did not contain intelligence assessments.
Its statement added: "The July document makes clear that our central planning assumption at the time was that the peace process in Afghanistan would run for up to a further six months."
media captionDominic Raab tells MPs intelligence suggested Kabul was unlikely to fall this year
The last UK plane flying people out of Kabul took off on Saturday, with the US following on days later to stick to the 31 August deadline pledged by US President Joe Biden.
The UK has evacuated around 15,000 people from Afghanistan since the country fell to the Taliban – but it is feared hundreds eligible for relocation were left behind.
Mr Raab said he believed the number of UK nationals still in Afghanistan was in the "low hundreds".
But he could not give a precise figure of the number of eligible Afghans who wanted to leave but were unable to get on evacuation flights.
These groups include Afghan nationals and their families who worked with British forces during their time in the country and asylum seekers who could be eligible to come to the UK under international law.