A US Air Force aircraft takes off from the airport in Kabul. AFP

As the final five US military transport aircraft lifted off out of Afghanistan, the Taliban were in full control of Kabul's international airport on Tuesday.

In a show of control, turbaned Taliban leaders were flanked by the elite Badri unit (special force) as they walked across the tarmac. The commandos in camouflage uniforms proudly posed for photos.

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Getting the airport running again is just one of the sizeable challenges the Taliban face in governing a nation of 38 million people that for two decades had survived on billions of dollars in foreign aid.

Taliban spokesman Zabihullah Mujahid  (centre) speaks to the media at the airport in Kabul on Tuesday. AFP

"Afghanistan is finally free,” Hekmatullah Wasiq, a top Taliban official, told The Associated Press on the tarmac. "The military and civilian side (of the airport) are with us and in control. Hopefully, we will be announcing our Cabinet. Everything is peaceful. Everything is safe.”

US have left behind up to 200 Americans and thousands of desperate Afghans who couldn't get out and now must rely on the Taliban to allow their departure.

The last US plane left its runway, marking the end of America's longest war and leaving behind a quiet airfield and Afghans outside it still hoping to flee the insurgents' rule.

Secretary of State Antony Blinken said the US will continue to try to get Americans and Afghans out of the country, and will work with Afghanistan’s neighbors to secure their departure either over land or by charter flight once the Kabul airport reopens.

Taliban Badri special forces secure the airport in Kabul on Tuesday. AFP

"We have no illusion that any of this will be easy, or rapid,” said Blinken, adding that the total number of Americans who are in Afghanistan and still want to leave may be closer to 100.

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.

The Taliban's top spokesman congratulated Afghans on their victory on Tuesday, hours after the last US troops left the country following 20 years of military intervention.

"Congratulations to Afghanistan... this victory belongs to us all," Taliban spokesman Zabihullah Mujahid said from the runway of Kabul airport.

A teacher conducts a class at a government middle school in Kabul. AFP

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

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.

Students arrive to attend their morning classes at a government middle school in Kabul on Tuesday. AFP

Zalmay Khalilzad, the US special representative who oversaw America’s talks with the Taliban, wrote on Twitter that "Afghans face a moment of decision & opportunity” after the withdrawal.

"Their country’s future is in their hands. They will choose their path in full sovereignty,” he wrote. "This is the chance to bring their war to an end as well.”

Schools have reopened, and on Tuesday morning dozens of elementary school students headed to schools in a neighbourhood near the airport. The Taliban have ordered schools to be segregated but it is often not enforced for younger children.

"I am not afraid of the Taliban,” said Masooda, a fifth-grade student.

During the evacuation, US forces helped evacuate over 120,000 US citizens, foreigners and Afghans, according to the White House. Coalition forces also evacuated their citizens and Afghans. But for all who got out, foreign nations and the US acknowledged they didn't evacuate all who wanted to go.