Around 16,000 people have been evacuated from Afghanistan through Kabul airport over the past 24 hours, the Pentagon has said, as international airlift operations sped up ahead of next week's deadline.

Pentagon spokesman John Kirby said that took the number of people reolcated from Afghanistan since July to 42,000, and 37,000 since the intense airlift operations started on 14 August as the Taliban moved to take Kabul.

It comes after a Taliban official said they will not agree to an extension of the 31 August deadline for the United States to withdraw troops and a delay will bring consequences.

"You can say it's a red line," spokesman Suhail Shaheen said in an interview on Sky News.

"If the US or UK were to seek additional time to continue evacuations - the answer is no. Or there would be consequences."

Western security forces were involved in an exchange of fire with unidentified gunmen at Kabul airport earlier, as US President Joe Biden sought to speed up the chaotic evacuation of tens of thousands of people from Taliban-controlled Afghanistan.

One Afghan was killed and three others were injured in a dawn firefight that according to the German military erupted between Afghan guards and unknown assailants.

German and US troops "participated in further exchange of fire", the German army said in a statement.

Britain's armed forces minister James Heappey said British forces or nationals were not involved in the firefight.

The Taliban, infamous for an ultra-strict interpretation of sharia law during their initial 1996-2001 rule, have repeatedly vowed a softer version this time.

However terrified Afghans continue to try to flee, overwhelming the operation at Kabul airport and leading to tragic scenes in which at least eight people have died.

A Taliban checkpoint in Kabul

The Taliban's victory ended two decades of war as they took advantage of Mr Biden's decision to withdraw nearly all US troops from the country.

Former Taoiseach John Bruton said Tony Blair was altogether wrong to call the Joe Biden slogan of "ending the forever war" in Afghanistan "imbecilic".

"It is not imbecilic. ALL wars have to end some time. Forever wars make no sense," he said in a statement.

"The literal implication of Tony Blair's criticism of Joe Biden is that the US should go on fighting in Afghanistan indefinitely. War aims should be precise, limited, and based on evidence.

"It appears that Tony Blair has not learned this....even yet."

Mr Biden had to redeploy thousands back to Afghanistan to oversee the evacuations but has insisted he wants to end the US military presence and the airlifts by 31 August.

However, with the European Union and Britain saying it would be impossible to get everyone out by then, Mr Biden is under pressure to extend the deadline.

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Speaking at the White House, Mr Biden said he hoped the airlift would not be extended, but said talks were under way to explore that possibility.

"There's discussions going among us and the military about extending," Mr Biden said.

He acknowledged the distressing scenes at the airport, which have included babies and children being passed to soldiers over razor-wire fences and men clinging to the outside of departing planes.

A child is lifted over razor-wire fence at Kabul airport (Pic: Omar Haidari/Reuters)

But he said they were part of the cost of departure.

"There is no way to evacuate this many people without pain and loss and heartbreaking images you see," he said.

In an effort to ramp up the airlift, the US government ordered six major commercial airlines to fly back to the United States those who have been evacuated from Kabul to US bases in the Gulf and Europe.

Overcrowding at those bases has slowed down, and occasionally stopped, the flights from Kabul.

Mr Biden spoke after the Taliban, who have been holding talks with elders and politicians to set up a government, slammed the evacuation.

"America, with all its power and facilities ... has failed to bring order to the airport," Taliban official Amir Khan Mutaqi said.

"There is peace and calm all over the country, but there is chaos only at Kabul airport."

British and Canadian soldiers help an Afghan climb up on the wall of a canal near the airport

In the streets of the capital, the Taliban have indeed enforced a calm of a kind, with their armed forces patrolling the streets and manning checkpoints.

Visually, they have also been looking to stamp their authority, ensuring the tri-coloured nation flag is replaced with their white banner.

At a roadside in Kabul at the weekend, young men sold Taliban flags, which bear in black text the Muslim proclamation of faith and the regime's formal name: "Islamic Emirate of Afghanistan".

"Our goal is to spread the flag of the Islamic Emirate throughout Afghanistan," said seller Ahmad Shakib, who studies economics at university.

Outside of Kabul, there have been flickers of resistance against the Taliban.

Some ex-government troops have gathered in the Panjshir Valley, north of the capital, which is long known as an anti-Taliban bastion.

Some pro-Taliban Twitter accounts said the new regime was sending hundreds of fighters to the valley after "local state officials refused to hand it over peacefully".

The Islamists have "massed forces near the entrance of Panjshir", tweeted Amrullah Saleh, vice president of Afghanistan in the previous government who has taken refuge in the area.

One of the leaders of the movement in Panjshir, named the National Resistance Front, is the son of famed anti-Taliban commander Ahmad Shah Massoud.

The NRF is prepared for a "long-term conflict" but is also still seeking to negotiate with the Taliban about an inclusive government, its spokesman Ali Maisam Nazary said in an interview over the weekend.

"The conditions for a peace deal with the Taliban is decentralisation, a system that ensures social justice, equality, rights, and freedom for all," he said.