The foreign secretary is set to hold talks with his Pakistani counterpart, Makhdoom Shah Mahmood Qureshi, as he attempts to build a coalition to exert “maximum moderating influence” on the Taliban.
It comes as former cabinet secretary Sir Mark Sedwill has warned that the UK and its allies still have no coherent plan to deal with the looming refugee crisis.
Sir Mark said the emergency airlift over the past two weeks “can’t and shouldn’t conceal that overall, we do not yet have a coherent policy and plan in place to deal with refugee flows out of Afghanistan”.
The Foreign Office announced a £30m UK aid package for Afghan refugees fleeing to neighbouring countries – with £10m going to relief efforts co-ordinated by groups such as the United Nations High Commissioner for Refugees (UNHCR).
Countries predicted to experience a significant increase in refugees will also receive £20m to help with processing new arrivals and to provide essential services and supplies.
Mr Raab arrives in Pakistan after Boris Johnson signalled further engagement between the West and the Taliban could be dependent on enabling the departures of Britons and Afghans left behind.
During a visit to Qatar on Thursday, Mr Raab said evacuations may be able to resume from Kabul airport “in the near future” as he expressed a need for direct engagement with the Taliban.
On Thursday evening, Mr Raab tweeted that he spoke to Tajikistan foreign minister Sirojiddin Muhriddin about “how our countries can help maintain stability in the region, and tackle the humanitarian situation in Afghanistan”.
More than 8,000 former Afghan staff and their family members eligible under the Afghan relocations and assistance policy (Arap) were among the 15,000-plus people evacuated by the UK since August 13.
But thousands of Afghans who helped British efforts in the nation and their relatives, as well as other vulnerable civilians, are feared to have been left behind.
Conservative MP Tom Tugendhat, chair of the Foreign Affairs Committee, warned that the end of the evacuation operation in Afghanistan was “only the beginning of a new stage of chaos”.
Justice secretary Robert Buckland said he was working to help more female judges in Afghanistan get out of the country. “So far we have managed to get nine female judges here to the UK,” he told Sky News on Friday.
Mr Buckland said: “A lot of these judges were responsible for administering the rule of law and quite rightly they are fearful for the consequences from the rise of the Taliban.”
The cabinet minister added: “I’m making sure that my officials are working hand in glove with the Foreign Office to identify as many as possible … and communicate with them to establish how to get safe passage for these very vulnerable people.”
Thousands of Afghans evacuated to Britain in recent weeks are set to be placed in temporary hotel accommodation for an indefinite period, as local councils say they have been left “in the dark” about how they can help.
Cllr David Touane, of South Oxfordshire District Council, said: “Many councils are ready to help but we are in the dark about what it is precisely that government wants us to provide.
As part of our Refugees Welcome campaign, The Independent has launched a petition urging the UK government to be more ambitious in its plans to take in Afghan refugees following the Taliban seizing power and withdrawal of western troops.