The Taliban are on the brink of taking full control of the Afghan capital, Kabul, after their fighters were ordered on Sunday afternoon to enter the city and the US sent helicopters to evacuate diplomats from its embassy.

In deeply humiliating scenes for the Biden administration, embassy personnel were ferried from the compound to the nearby airport by military helicopter. Diplomatic armoured SUVs were also seen leaving. The exodus began early on Sunday after the insurgents captured the eastern city of Jalalabad.

Wisps of smoke from the embassy roof were visible across the city, residents said, as diplomats urgently destroyed sensitive documents. At the airport, contractors, diplomats and civilians eligible to fly out were given special bracelets, the New York Times reported. British embassy staff were also scrambling to leave the country, including the ambassador.

The US secretary of state, Anthony Blinken, said the US was moving its embassy compound to the airport.

As events unfolded with dizzying speed Afghanistan’s pro-western president, Ashraf Ghani, fled to neighbouring Tajikistan, according to multiple reports. Diplomatic sources said he had resigned. His office said it could not comment on his movements for security reasons.

Within hours of his apparent departure, Taliban officials said their fighters had been instructed to go into the city centre in order to “maintain law and order”. The insurgents would not enter civilian homes or harass residents, a statement declared.

With negotiations over a transition of power taking place in Doha, there was speculation that the Taliban leader, Mullah Abdul Ghani Baradar, would become the country’s new president, possibly by Sunday evening.

The US was seeking agreement from the Taliban on a peaceful transition of power, as well as assurances on refugees and that the new government would not impose sharia law, diplomats said. Washington’s ability to influence events is, however, severely limited. Pakistan and Iran are the main external players.

The Taliban’s stunning 11-day offensive across Afghanistan appears to be entering its final, dramatic phase. Its fighters have captured a string of provincial capitals. On Sunday they took up positions on the outskirts of Kabul and the districts of Kalakan, Qarabagh and Paghman.

Taliban leaders said they had no plans to seize the capital by force. Instead, by lunchtime small groups of fighters entered the city from two directions .One column, apparently unarmed and holding the white Taliban flag, was spotted marching towards the presidential palace.

Other fighters broke out prisoners from Pul-e-Charkhi, Afghanistan’s biggest military-run detention facility. Video showed them streaming out with their possessions. By Sunday afternoon the fall of Kabul and its western-backed government seemed a mere formality, just a few hours away.

The outgoing Afghan government led by Ghani appears to have recognised this rapidly unfolding reality. The acting interior minister, Abdul Sattar Mirzakwal, said in a tweet that a peaceful transition to Taliban rule was underway. Kabul would not be attacked, he said.

Despite sporadic gunfire, the insurgents appear to have met little or no resistance. Their coordinated entry into Kabul follows the capture on Saturday of Mazar-i-Sharif, Afghanistan’s fourth biggest city and the last major government stronghold in the north.

Kabul airport is now the only exit point under government control after the fall of Jalalabad in the east. The Taliban also advanced to the nearby Torkham border crossing, which Pakistan has shut.

The Taliban’s spokesman said on Sunday that the group did not intend to take reprisals against Afghans living in Kabul who had worked with the US or who had served in the Afghan military.

Zabihulla Mujahid tweeted: “We don’t want a single, innocent Afghan civilian to be injured or killed as we take charge.” He added, however: “We have not declared a ceasefire.”

The likely imminent fall of Kabul amounts to a disastrous moment for western policy, two decades in the making. An international coalition led by Washington and London triumphantly pushed out the Taliban in December 2001, seemingly consigning their caliphate to history.

The country is set to revert to hardline Islamist rule, and the gains made in the realm of women and girls’ education are set to disappear overnight. Photos from Kabul showed workmen erasing photos in shop windows of women in wedding dresses. And despite the conciliatory tone of recent Taliban messaging, reprisals in Kabul seem likely.

The mood on the streets was one of fear, residents said. Shops remain closed and citizens tried to withdraw their savings from banks. People displaced from other parts of the country as the Taliban advanced are camped out in parks and public spaces, huddled in tents.

The rapid collapse of the pro-western government follows Joe Biden’s decision in May to pull out US troops. The speed of the Taliban’s advance, however, and the utter capitulation of the Afghan military appear to have taken Washington by surprise.

A US intelligence estimate just last week said Kabul could hold out for at least three months. Instead, diplomatic personnel were dashing to the airport on Sunday, where they set up a temporary embassy base. Nato officials said EU staff had also relocated to a safer, undisclosed location in the capital.

Biden has authorised the deployment of 5,000 troops to help evacuate citizens and ensure an “orderly and safe” drawdown of military personnel. A US defence official said that included 1,000 newly approved troops from the 82nd Airborne Division.

The Taliban captured the eastern city of Jalalabad without a fight earlier on Sunday, giving them control of one of the main highways into landlocked Afghanistan.

“There are no clashes taking place right now in Jalalabad because the governor has surrendered to the Taliban,” a Jalalabad-based Afghan official told Reuters. “Allowing passage to the Taliban was the only way to save civilian lives.”

A video clip distributed by the Taliban showed people cheering and shouting “Allahu Akbar” or “God is greatest” as a convoy of pickup trucks entered the city with fighters brandishing machine guns and the white Taliban flag.

The insurgents entered Mazar-i-Sharif virtually unopposed as security forces escaped up the highway to Uzbekistan, about 50 miles (80km) to the north, provincial officials said. Unverified video on social media showed Afghan army vehicles and men in uniforms crowding the iron bridge between the Afghan town of Hairatan and Uzbekistan.

Two influential militia leaders supporting the government – Atta Mohammad Noor and the veteran warlord Abdul Rashid Dostum – also fled. Noor said on social media that the Taliban had been handed control of Balkh province, where Mazar-i-Sharif is located, as a result of a “conspiracy”.

The Taliban said in a statement late on Saturday that its rapid gains showed they were popular and accepted by the Afghan people and reassured both Afghans and foreigners that they would be safe.

The Islamic Emirate, as the Taliban call themselves, “will, as always, protect their life, property and honour, and create a peaceful and secure environment for its beloved nation”, they said, adding that diplomats and aid workers would also face no reprisals.