The defeat of America was a "big lesson for other invaders and for our future generation", the Taliban said on Tuesday, hours after the last foreign troops departed Afghanistan.

"It is also a lesson for the world," spokesman Zabihullah Mujahid said from the runway of Kabul Airport.

The Taliban's top spokesman congratulated Afghans on their victory. "Congratulations to Afghanistan... this victory belongs to us all," Zabihullah Mujahid said.

"We want to have good relations with the US and the world. We welcome good diplomatic relations with them all," he added.

Welcoming the US withdrawal from Afghanistan, Zabihuallah Mujahid wrote on twitter "In this way, our country became completely free and independent."

See Also: Celebratory gunfire as last US troops exit Afghanistan, ending 20-year war

Shortly after Mujahid's comments on social media, Taliban members started celebratory gun firing in the capital Kabul, which lasted for about an hour, causing panic among local residents.

Following the firing, Mujahid said in a separate tweet that "the gunshots heard in Kabul are as a result of celebratory firing, the Kabul residents should not worry, we are trying to control it."

The capital city Kabul is calm "like other normal days," but a U.S. unmanned plane has been spotted flying over the city, witnesses in Kabul told Xinhua.

The Taliban hailed the departure of US troops after almost 20 years of occupation, describing their departure as a “historic moment” while declaring that the country is now a “free and sovereign nation”.

Speaking to reporters from Hamid Karzai International Airport, Taliban spokesman Zabihullah Mujahid said the victory of his group “belongs to us all”.

“We do not have any doubt that the Islamic Emirate of Afghanistan is a free and sovereign nation,” he said, adding the Americans “could not achieve their goal through military operations”.

He also vowed that Afghanistan will have “working diplomatic relations” with the West, vowing that Afghans “will protect our freedom, independence and Islamic values.”

See Also: Taliban ‘launch’ attack on Panjshir Valley

A senior Taliban leader said the Taliban had "made history", as celebratory gunfire was heard across the Afghan capital after the last US troops pulled out.

"We made history again. The 20-year occupation of Afghanistan by the United States and NATO ended tonight," said Anas Haqqani, a senior official in the hardline movement, in a tweet. "I am very happy that after 20 years of jihad, sacrifices & hardships I have this pride to see these historic moments."

Taliban celebrate

The Taliban joyously fired guns into the air and offered words of reconciliation on Tuesday, as they celebrated defeating the United States and returning to power after two decades of war that devastated Afghanistan.

The last of 6,000 US troops who oversaw a desperate evacuation effort flew out of Kabul airport on Monday night, ending the war that has diminished the United States' status as a superpower.

Taliban fighters quickly swept into the airport and fired weapons into the sky in jubilation, an astonishing return after US forces invaded in 2001 and toppled the hardline Islamists for supporting Al-Qaeda.

"Congratulations to Afghanistan... this victory belongs to us all," Taliban spokesman Zabihullah Mujahid told reporters hours later from the runway of the airport.

Mujahid said the Taliban's victory was a "lesson for other invaders".

However the Taliban have repeatedly promised a more tolerant and open brand of rule compared with their first stint in power, and Mujahid continued that theme.

"We want to have good relations with the US and the world. We welcome good diplomatic relations with them all," he said.

Many Afghans are terrified of a repeat of the Taliban's initial rule from 1996-2001, which was infamous for their treatment of girls and women, as well as a brutal justice system.

- Terror threat -

The withdrawal came just before the end of an August 31 deadline set by President Joe Biden to call time on America's longest war -- one that ultimately claimed the lives of more than 2,400 US service members.

The early finish followed a threat from the regional offshoot of the Islamic State group, rivals of the Taliban, which was seeking to attack the US forces at the airport.

Thirteen US troops were among more than 100 people killed when an IS suicide bomber late last week attacked the perimeter of the airport, where desperate Afghans had massed in the hope of getting on board an evacuation flight.

More than 123,000 people were evacuated from Kabul aboard the US-led airlift operation, which began just after the Taliban swept into the capital on August 14.

Biden said he would address the nation on Tuesday in Washington, as his critics continued to savage him for his handling of the withdrawal.

"We can't fight endless wars, but the scope & consequence of Biden's failure here is staggering," Republican Senator Rick Scott said.

"President Biden has brought great shame on the American people," added congressman Richard Hudson.

Biden's top diplomat, Secretary of State Antony Blinken, was able to offer little more than stern words for the Taliban.

"Any legitimacy and any support will have to be earned," Blinken said, as he announced the United States had suspended its diplomatic presence in Kabul and shifted its operations to Qatar.

- Airport uncertainty -

All eyes will now turn to how the Taliban handles its first few days with sole authority over the country, with a sharp focus on whether it will allow other foreigners and Afghans to leave the country.

Blinken said a small number of US citizens remained in the country -- "under 200" but likely closer to just 100 -- and wanted to leave.

Many thousands of other Afghans who had worked with the US-backed government and fear retribution also want to get out.

Western allies have voiced heartbreak in recent days that not all Afghans who wanted to flee could get on the evacuation flights.

The UN Security Council adopted a resolution Monday, requiring the Taliban to honour a commitment to let people freely leave Afghanistan in the days ahead, and to grant access to the UN and other aid agencies.

But they did not agree to call for the creation of a "safe zone" in Kabul, as envisaged by French President Emmanuel Macron.

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

The Taliban have asked Turkey to handle logistics while they maintain control of security, but President Recep Tayyip Erdogan has not yet accepted that offer. 

It was not immediately clear which airlines would agree to fly in and out of Kabul.

- Civilian deaths -

The regional Islamic State-Khorasan (IS-K) group had posed the biggest threat to the withdrawal after it carried out the devastating suicide bombing outside the airport last week.

On Monday, they also claimed to have fired six rockets at the airport. A Taliban official said the attack was intercepted by the airport's missile defence systems.

And in an echo of the tragedies of civilian deaths that plagued the war and cost the United States local support, a US air strike in Kabul targeting a purported IS car bomb on the weekend appeared to have killed children.

The United States said Sunday it had carried out a drone strike against a vehicle threatening the Kabul airport. 

Members of one family told AFP they believed a fatal error had been made, and that 10 civilians were killed.

"My brother and his four children were killed. I lost my small daughter... nephews and nieces," Aimal Ahmadi told AFP.–Agencies