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The US has suggested that its forces may have to remain in the country beyond that date to fly Americans out of the capital Kabul.
But the Taliban are opposed to any delay spokesman and spokesman Suhail Shaheen said there would be consequences if foreign forces stayed longer.
“It's a red line. US President Joe Biden announced that on 31 August they would withdraw all their military forces, so if they extend it that means they are extending occupation while there is no need for that,” he told Sky News on Sunday.
“If the US or UK were to seek additional time to continue evacuations, the answer is no. Or there would be consequences.
“It will create mistrust between us. If they are intent on continuing the occupation, it will provoke a reaction."
Since the Taliban seized control of the country on August 15, Washington and its allies have flown about 28,000 people out of Afghanistan.
The US military has said it can fly more than 9,000 people out of Kabul every day.
The US has either flown or aided efforts to take about 42,000 people out of Afghanistan since the end of July, the official said.
The US is currently running Kabul airport and is co-ordinating the international evacuation effort.
“We see no reason why this tempo will not be kept up,” Mr Biden said on Sunday.
“What I’m not going to do is talk about the tactical changes we’re making to make sure we maintain as much security as we can.
“We have constantly, how can I say it, increased rational access to the airport, where more folk can get there more safely.
"It’s still a dangerous operation, but I don’t want to go into the detail of how we’re doing that.”
He later said the Taliban had been "co-operative in extending some of the perimeter" at the airport.
He could hold discussions about keeping US forces in Afghanistan beyond this month.
“Our hope is we will not have to extend, but there are going to be discussions, I suspect, on how far along we are in the process,” he said.
Australia is willing to support an extension to the withdrawal deadline if Washington backed the move, Foreign Minister Marise Payne said on Monday.
The UK Defence Ministry has released footage of British and US forces working together to keep Kabul airport secure as the evacuation effort continues.
On Sunday, troops were seen patrolling the perimeter as crowds of Afghans waited outside the airport's walls.
It also released an image of dozens of exhausted Afghans boarding a Royal Air Force C-17 transport aircraft.
British military personnel have been helping Afghans who are eligible for be relocated to the UK under the Afghan Relocation and Assistance Policy, the ministry said.
On Monday, Japan said it would send a military aircraft to Afghanistan to bring back its citizens.
More military transport planes are expected to be arrive to repatriate Japanese and Afghans who worked at the Japanese embassy or with Japanese missions, said Chief Cabinet Secretary Katsunobu Kato.
“This transportation is an urgent humanitarian measure to evacuate our nationals in such an exceptional situation,” he said.
Meanwhile, the World Health Organisation said it was unable to deliver 500 tonnes of medical supplies to Afghanistan because of flight restrictions at Kabul airport.
The shipment, which includes surgical equipment and childhood pneumonia treatments, was scheduled to be delivered this week.
“Now that the airport is closed to commercial flights, we can no longer get them in,” WHO spokeswoman Inas Hamam told Reuters.
The WHO has called for empty aircraft to divert to its storage centre in Dubai to collect the supplies before picking up people fleeing Afghanistan.
Biden faces backlash
Mr Biden has faced criticism at home and abroad over the deteriorating situation in Afghanistan, with US National Security Adviser Jake Sullivan saying on Monday that ISIS could be active near Kabul airport.
Republicans in Congress have increased their condemnation of Mr Biden’s response to the crisis in Afghanistan.
“If the Taliban is saying that Americans can travel safely to the airport, then there is no better way to make sure they get safely to the airport than to use our military to escort them,” Joni Ernst, a senator for Iowa and a military veteran, told ABC.
Ryan Crocker, who served as US ambassador to Afghanistan under presidents George W Bush and Barack Obama, told CBS that Mr Biden’s management of the withdrawal was catastrophic and unleashed a “global crisis".
Vice President Kamala Harris was also given plenty of reminders of the situation in Kabul during her visit to Singapore.
She faced several questions about the Biden administration's response during a joint press conference with Prime Minister Lee Hsien Loong.
Ms Harris said that while there “will be and should be a robust analysis of what has happened", the focus had to be on efforts to help “American citizens, Afghans who worked with us and vulnerable Afghans, including women and children".
“We cannot be in any way distracted from what must be our primary mission right now, which is evacuating people from that region who deserve to be evacuated,” she said.