DOHA (AFP) - The Qatari and German foreign ministers warned on Tuesday (Aug 31) against any rise of terrorism after the US withdrawal from Afghanistan, now under Taliban rule.

Qatar's foreign minister, Sheikh Mohammed bin Abdulrahman al-Thani, urged the hardline group to combat terrorism, calling for an inclusive government.

"We stressed the importance of cooperation to combat terrorism... and we stressed the importance of the Taliban to cooperate in this field," he said in a press conference after meeting with his German counterpart, Heiko Maas.

"It is our role to always urge them (Taliban) to have an expanded government that includes all parties and not to exclude any party.

"During our talks with the Taliban, there was no positive or negative response," al-Thani said, referring to recent talks between Qatar and Afghanistan's new rulers.

Taliban fighters celebrated with gunfire on Tuesday hours after the last US forces abandoned Kabul, closing a frenzied airlift operation that saw more than 123,000 foreign nationals and Afghans flee.

Maas, in turn, said he saw "no way around" talking with the Taliban.

"I personally believe there is absolutely no way around having talks with the Taliban... because we absolutely cannot afford to have instability in Afghanistan," he said.

"That would aid terrorism and have a huge negative impact on neighbouring countries.

"We are not looking at questions of formal recognition, but we want to solve the existing problems - regarding the people in Afghanistan, the German citizens, but also the local staff who want to leave the country."

Earlier, German Chancellor Angela Merkel said keeping Kabul airport open was of "existential importance", as Western nations now consider how to get more people out of the country.

Talks are ongoing as to who will now run Kabul airport.

US officials have said the airport is in a bad condition, with much of its basic infrastructure degraded or destroyed.

The Taliban have asked Turkey to handle logistics while they maintain control of security, but President Recep Tayyip Erdogan appeared to pour cold water on that idea on Sunday.

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 attacking them.

Qatar, the UAE, Kuwait and Bahrain have been instrumental staging posts for evacuation flights for Western countries' citizens as well as Afghan interpreters, journalists and others.

Britain and the US have said they will operate their Afghan missions from Doha.