Qatar on Wednesday urged the Taliban to ensure "safe passage" for people still wanting to leave Afghanistan after the chaotic US-led evacuations came to an end.
More than 123,000 foreign nationals and Afghans fled the country in a frenzied airlift operation that wound up on Tuesday, but many more are desperate to depart.
"We stress on the Taliban the issue of freedom of movement and that there be safe passage for people to leave and enter if they so wish," Qatari Foreign Minister Sheikh Mohammed bin Abdulrahman al-Thani told a press conference after a meeting with his Dutch counterpart, Sigrid Kaag.
"We hope to see these commitments fulfilled in the near future when the airport begins operations again and that it happens smoothly, with no obstacles for anyone wanting to leave or come to Afghanistan."
US officials have said Kabul airport is in a bad condition, with much of its basic infrastructure degraded or destroyed.
Taliban fighters celebrated with gunfire on Tuesday after the last US forces abandoned Kabul following a two-decade war.
Kaag said the Netherlands will move its Kabul diplomatic mission to Qatar, following similar moves by the United States and Britain.
Qatar hosted negotiations between the Taliban and the United States in recent years and was a transit point for about 43,000 evacuees from Afghanistan.
"I've asked his excellency very kindly agree to the relocation of the Netherlands embassy from Kabul to Doha," Kaag told journalists.
She also stressed "the importance of ensuring that Afghanistan no longer resumes to become a base for terrorist organizations".
"I've also asked (the Qatari foreign minister) to employ his influence and context to really help all parties in Afghanistan, to reach an inclusive political agreement that ensures stability and future prosperity."
The US invaded Afghanistan and toppled its Taliban government in 2001 in the wake of the 9/11 attacks by Al-Qaeda, which had sought sanctuary in the country.
Western capitals fear Afghanistan could again become a haven for extremists bent on attacks.
Gulf countries, including Qatar, have been instrumental staging posts for evacuation flights for Western countries' citizens as well as Afghan interpreters, journalists and others.