Mr Raab will discuss the feasibility of a functioning airport in Kabul – either for charter or commercial flights – and the safe passage of foreign nationals and Afghans across land borders.
While in Qatar, he will also meet the Amir of Qatar, Sheikh Tamim bin Hamad al Thani, and deputy prime minister and foreign minister Sheikh Mohammed bin Abdulrahman al Thani.
The British Embassy to Afghanistan has been temporarily relocated and is now up and running in Doha.
The foreign secretary will meet Dr Martin Longden, who arrived in Qatar on Wednesday and is temporarily in charge while the ambassador, Laurie Bristow, takes a short time off following his efforts assisting the UK’s evacuation.
Mr Raab left the UK hours after he was questioned by MPs in the Foreign Affairs Select Committee on the events in central Asia.
He said he was “not confident with any precision” on how many people eligible to come to the UK were left in Afghanistan – although he claimed the number of British nationals is in the “low hundreds”.
The UK has said it is keen to work with Qatar and other international partners to ensure the Taliban government bear down on terrorist threats, facilitate humanitarian access and protect human rights – especially those of women and girls.
Before he left the country, the foreign secretary spoke to his Indian counterpart Dr Subrahmanyam Jaishankar and thanked him for helping to secure a UN Security Council resolution on Afghanistan.
Meanwhile, Prime Minister Boris Johnson is expected to travel to South East England to visit the troops who assisted in the evacuation from Kabul.
Qatar was the home to the Taliban‘s political operation from 2013 and is encouraging dialogue with the militants despite not recognising them as the government of Afghanistan.
Meanwhile, Foreign Office minister Lord Ahmad of Wimbledon will travel to Tajikistan to talk about the safety of those entering the country from neighbouring Afghanistan.
A leaked document, seen by ministers on 22 July and now shown to Sky News, warned the government that the withdrawal of US troops from Afghanistan would lead to “rapid Taliban advances”.
The Conservative chairman of the Foreign Affairs Committee, Tom Tugendhat, read extracts of the Principal Risk Register report to MPs as Mr Raab was questioned for almost two hours about the UK’s withdrawal from Afghanistan.
The document had stressed the move could lead to “the fall of cities”, the “collapse of security forces” and that the embassy “may need to close if security deteriorates”.
Asked about the report, Mr Raab told the committee: “The central assessment that we were operating to – and it was certainly backed up by the JIC (Joint Intelligence Committee) and the military – is that the most likely, the central proposition, was that given the troop withdrawal by the end of August, you’d see a steady deterioration from that point, and it was unlikely Kabul would fall this year.”
A spokesperson for the Foreign Office said it is “simply wrong and misleading to suggest this document is any way at odds with our detailed assessments of the situation in Afghanistan or our public position throughout the crisis”.