The militants are on the brink of taking total control, after rapidly seizing territory as US-led forces withdrew after 20 years of operations.
Thousands of Afghans have sought refuge in Kabul in recent weeks and there were scenes of panic in the city on Sunday.
A Taliban spokesman told the BBC there would be “no revenge” on Afghans.
Western countries have been scrambling to evacuate their citizens. The US sent military helicopters to transport staff from its heavily fortified embassy compound to the airport.
However, the US Embassy later said there were reports of gunfire at Kabul’s airport. It warned US citizens in the area to take shelter as “the security situation… is changing quickly”.
It is almost 20 years since the Islamist group was ousted by a US-led military coalition. Their advance across the country began months ago but has accelerated in the space of days.
US President Joe Biden has defended the withdrawal of American troops, saying he could not justify an “endless American presence in the middle of another country’s civil conflict”.
‘People are running and hiding’
Taliban spokesman Zabihullah Mujahid said militants had been ordered to enter parts of Kabul on Sunday, after previously holding back at the outskirts of the city.
He said Taliban fighters were going in to prevent chaos and looting after security forces left parts of the city.
The Taliban later said they were in control of around half of the city’s districts.
Their advance into Kabul came after President Ghani fled.
Details of his whereabouts remain unknown, but some reports said he was heading for Tajikistan.
In a Facebook post addressed to Afghan citizens, Mr Ghani said he made the difficult decision to leave to avoid bloodshed in the capital city of six million people.
But other Afghan officials criticised the move.
“God will hold him accountable and the nation will also judge,” said Abdullah Abdullah, chairman of Afghanistan’s High Council for National Reconciliation.
Afghan people line up outside AZIZI Bank to take out cash as the Bank suffers amid money crises in Kabul, Afghanistan, on August 15, 2021.
There was panic in Kabul as the Taliban drew closer to victory. Residents headed for the airport, abandoning cars and making their way on foot in a desperate bid to get out of the country.
One 22-year-old student told the BBC that he had walked for more than five hours.
“My feet hurt, they have blisters and I’m finding it difficult to stand,” he said.
“Now that I’m leaving, I think about my family – they don’t have any way to escape. I don’t see a future.”
An eyewitness at the airport told the BBC the departure hall had “turned into chaos”, and described people running across the tarmac to planes and staff abandoning their desks.
A Nato official later said that all commercial flights out of Kabul had been suspended.
A US military helicopter is pictured flying above the US embassy in Kabul.
The US has sent military helicopters to evacuate embassy staff.
In the city centre, large queues formed at ATMs throughout the day as people sought to withdraw cash.
Taliban spokesman Suhail Shaheen told the BBC that people in Kabul had no need to worry and that their properties and lives were safe.
“We are the servants of the people and of this country,” he said.
A rush to evacuate civilians
The US has deployed 5,000 troops to help remove its staff and the Afghans who assisted with
About 600 British troops have been deployed to assist with their own withdrawal mission.
UK Prime Minister Boris Johnson said his priority was getting UK nationals and “all those who have helped the UK effort over 20 years” out of Afghanistan “as fast as we can”.
He called on “like-minded” powers to work together and not recognise any new government without agreement.
Source: www.bbcnews.com