US President, Joe Biden, has defended the US withdrawal, saying he could not justify an “endless American presence in the middle of another country’s civil conflict”.
There is panic in Kabul, where some residents have been trying to reach the airport to leave the country. Cars have been abandoned and people have opted to walk because of traffic jams.
One 22-year-old student told the BBC that he had walked more than five hours to reach the airport.
“My feet hurt, they have blisters and I’m finding it difficult to stand,” he said.
“It was like a military town – people were in traditional clothes, but they had weapons and were firing in the air. It reminded me of the jihad that I heard of from my parents.”
Residents have also been rushing to withdraw cash from ATMs, and queuing to get travel documents at the passport office and at foreign visa centres.
Farzana Kocha, an MP in Kabul, told the BBC that people did not know what to do as Taliban militants closed in on the city.
“Some of them are running, some are hiding in houses,” she said.
Taliban spokesman Zabihullah Mujahid said militants had been ordered to enter some parts of Kabul on Sunday, after previously waiting on the outskirts.
He said Taliban forces were going in to prevent chaos and looting after security forces left parts of the city and their checkpoints.
Earlier on Sunday, the Taliban said they had taken control of Bagram airfield and prison, about 40km (25 miles) north of the city centre.
Once the largest American military facility in Afghanistan, the complex was evacuated by the US military in the dead of night on 2 July.
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.
He added that the group did not want Afghans to flee, but instead to stay and help with the post-conflict reconstruction.