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President fled Afghanistan on Sunday, a top official said, effectively ceding power to the as they reached the capital to seal a nationwide military victory in just 10 days.

"The former Afghan President has left the nation, leaving the people to this situation," Abdullah Abdullah, who heads the peace process, said in a video on his Facebook page.

"God hold him accountable, and the people will have their judgement."

He gave no indication where Ghani was going, but leading Afghan media group TOLOnews suggested he was heading to Tajikistan.

Ghani's departure from office was one of the key demands of the Taliban in months of peace talks with the government, but he had stubbornly .

In just over a week, the Taliban have carried out a lightning sweep of the country, with troops incapable of holding onto territory without US military support.

The insurgents said they want a "peaceful transfer", two decades after US-led forces toppled it in the wake of the September 11, 2001 attacks.

The group ordered its fighters earlier Sunday not to enter the capital, saying the remnants of the government's forces were responsible for security.

But later, a spokesman tweeted that Taliban forces should enter areas deserted by Afghan forces in order to maintain law and order.

"God forbid the common thieves and robbers in Kabul do not mix, the abusers do not harm the people, the Islamic Emirate ordered its forces to enter the areas of Kabul from which the enemy went," a statement by the Taliban said.

"There is a risk of theft and robbery."

There are fears of a security vacuum in the capital as thousands of police and other armed services members have abandoned their posts, uniforms, and even weapons.

The United States began moving its citizens and Afghan staff to Kabul airport, with the help of thousands of troops deployed to the capital to assist with the evacuation.

However, Secretary of State on Sunday dismissed comparisons with the chaotic American departure from Saigon in 1975.

"The fact of the matter is this: We went to Afghanistan 20 years ago with one mission in mind," he said.

"That was to deal with the people that attacked us on 9/11. That mission has been successful."

The Taliban's imminent takeover triggered fear and panic in Kabul among residents fearful of the group's hardline brand of Islam.