- War in Afghanistan (2001-present)
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The foreign secretary is urging his international counterparts to work together to provide safe passage for eligible people out of Afghanistan.
Dominic Raab said the Taliban would have to be judged on their actions, having promised those with authorisation would be allowed to leave, the Foreign Office said.
Troops have arrived back in the UK after British-led evacuations ended.
But the government says it will still help those eligible for resettlement.
Mr Raab's comments came at a US-chaired virtual meeting for representatives from his G7 counterparts – including the US, Canada, Japan, Germany, France and Italy – as well as Nato and the EU on Sunday.
Turkey and Qatar – considered to have more influence over the Taliban than Western nations – also attended.
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"The foreign secretary emphasised the importance of working with like-minded partners on safe passage and exit arrangements for eligible Afghans remaining in the country," said the Foreign, Commonwealth and Development Office (FCDO).
"He affirmed Taliban assurances that foreign nationals and Afghan citizens with travel authorisation will be allowed to depart the country, but underlined we must judge them on their actions, and whether people are allowed safe passage to leave."
He also highlighted the need to work "with a range of international partners in order to exercise the maximum moderating influence on the Taliban".
Mr Raab said preventing Afghanistan becoming a haven for terrorists was a priority, along with stability in the region and the need to protect human rights, said the FCDO.
The final stages of the evacuation from Kabul airport are currently under way ahead of the 31 August deadline for the US withdrawal from Afghanistan.
media captionThe final flights bringing British troops are arriving in the UK
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 people were unable to get on evacuation flights.
United Nations diplomats, including the UK's UN ambassador, Dame Barbara Woodward, are currently discussing a draft security council resolution. The resolution would urge the Taliban to ensure safe passage to those wanting to leave Afghanistan.
Along with France and the US, the UK wants the support of China and Russia to present a united message to Afghanistan's new government.
'Willing to engage'
Earlier, Prime Minister Boris Johnson said the UK and its allies would "engage with the Taliban not on the basis of what they say but what they do".
"If the new regime in Kabul wants diplomatic recognition, or to unlock the billions that are currently frozen, they will have to ensure safe passage for those who wish to leave the country, to respect the rights of women and girls, to prevent Afghanistan from, again, becoming an incubator for global terror, because that would be disastrous for Afghanistan," he said.
Foreign Office minister James Cleverly told the BBC the UK was "willing to engage" with the Taliban – but he could not give "absolute assurances" to those left behind.
"If [the Taliban] start acting like a government, if they start facilitating both internal travel and exiting from Afghanistan, then we will engage with them on that basis," he said.
"But of course what we are not able to do, what no country is ever really able to do, is give an absolute cast-iron guarantee."
Labour's shadow foreign affairs minister, Stephen Kinnock, said the government had been "asleep at the wheel" when it came to getting people out of Afghanistan.
"We have to now face the reality, unpalatable as it is, that some cooperation is going be required. What that means is cooperation with conditions," he said.
For those remaining in the country, Afghanistan could be on the brink of humanitarian disaster if international non-governmental organisations (NGOs) are forced to pull out, former international development secretary Rory Stewart warned.
"The Afghan government, which is now obviously the Taliban government, is running out of money," he said. "It's going to be very difficult to keep the water supply and electricity going. Much of the healthcare and education in the country is delivered by foreign NGOs and agencies."
What happens to Afghan refugees coming to the UK?
- Arrivals on official flights enter a 10-day Covid quarantine in a hotel
- Government officials and local authorities are trying to find them permanent homes
- A shortage of suitable accommodation means many will be placed in hotels
- Some will get refugee status and can live in the UK permanently
- Others will get a five-year visa to live and work in the UK – and can then apply for permanent residence
- Afghans arriving independently will enter the normal system for asylum claims – which has a backlog of 70,000 people
- These people cannot settle, or work, while their claims are considered
The talks come after survivors of a US drone strike targeting a suicide bomber told the BBC the attack ended up killing 10 members of one family, including six children.
Pentagon press secretary John Kirby they were "not in a position to dispute" the reports of civilian casualties and they were "assessing and… investigating".
He said there had been a "very real, a very specific and a very imminent threat" to Kabul airport from IS-K (Islamic State Khorasan Province), IS's Afghan affiliate, ahead of Sunday's strike.
The US had been on high alert since a suicide bomber killed more than 100 people outside the airport last Thursday. Among the dead were two British nationals, and the child of a British national.
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