The Taliban were attempting to demonstrate they control the areas around the chaotic Kabul airport on Sunday, where Nato said 20 people died in the past week.

As witnesses reported Taliban fighters to be firing into the air and using batons to force people to form orderly queues outside the main gates and not gather at the perimeter, the militant group that retook the Afghan capital last week after 20 years said it was seeking “complete clarity” on the evacuation plan being led by foreign forces.

It was not clear, however, whether the Taliban’s increasingly organised presence around the airport would also result in it controlling who is able to enter the airport and leave the country as the group’s spokesmen used the situation at the airport to criticise the US.

In an audio clip posted online, Amir Khan Motaqi, the chief of the Taliban’s guidance council, described US actions as “tyranny” – though it is Taliban fighters who have beaten and shot at those trying to access the airport over the last week.

“All Afghanistan is secure, but the airport which is managed by the Americans has anarchy,” he said. “The US should not defame itself, should not embarrass itself to the world and should not give this mentality to our people that [the Taliban] are a kind of enemy.”

At least 20 people have died in the past seven days in and around Kabul airport during the evacuation effort that was triggered when Taliban insurgents took over the Afghan capital last week, a Nato official said on Sunday.

“The crisis outside the Kabul airport is unfortunate. Our focus is to evacuate all foreigners as soon as we can,” said the official, who sought anonymity.

The deaths come as a new, perceived threat from the Islamic State affiliate group in Afghanistan has led US military planes to perform rapid, diving combat landings at the airport, which is surrounded by Taliban fighters.

Other aircraft have fired flares on takeoff, a tactic often used to confuse possible heat-seeking missiles targeting the planes.

A Nato official also appeared to concede the risks in the Taliban’s increased assertion of control beyond the airport’s perimeter saying: “Our forces are maintaining strict distance from outer areas of the Kabul airport to prevent any clashes with the Taliban.”

A journalist on board an evacuation convoy that left a downtown Kabul hotel early on Sunday told AFP that a huge crowd of Afghans was camped at an intersection close to the airport – many sleeping in the open – who mobbed the buses with their documents, asking to be let on.

Families hoping to escape were crowded between the barbed-wire boundaries of an unofficial no man’s land separating Taliban fighters from US troops and the remnants of an Afghan special forces brigade helping them.

“As soon as they saw our convoy, they got up and ran towards the buses,” he said.

The latest Taliban moves came as Afghan government forces forming a resistance movement in a fortified valley in the Panjshir region said they were preparing for “long-term conflict” if the Taliban refused to negotiate.

Pictures taken by AFP during training exercises show dozens of recruits performing fitness routines, and a handful of armoured Humvees driving across the valley north-east of Kabul.

With the Taliban moving to assert its control over the country, a week after seizing power, the group called for the reopening of schools and colleges and said it would meet with provincial governors across the country.

“We are not forcing any former government official to join or prove their allegiance to us, they have a right to leave the country if they would like,” said a Taliban official, who spoke on the condition of anonymity.

“We are seeking complete clarity on foreign forces’ exit plan,” he added. “Managing chaos outside Kabul airport is a complex task.”

The UK Ministry of Defence said “conditions on the ground remain extremely challenging but we are doing everything we can to manage the situation as safely and securely as possible.”

The evacuation of foreigners and Afghans linked to foreign countries remained fraught on Sunday after the US and Germany warned citizens to avoid travelling to Kabul airport, citing security risks including from thousands of desperate people gathered trying to flee from the Taliban and Isis.

Facing mounting criticism over his handling of the Afghanistan crisis, the US president, Joe Biden, who has defended his decisions, was due to speak again on Sunday to update the evacuation efforts.

The Taliban’s swift takeover of Afghanistan has sparked fear of reprisals and a return to the harsh version of Islamic law the Sunni Muslim group exercised when it was in power two decades ago.

Crowds have grown in hot and dusty areas around the airport over the past week, hindering operations as the United States and other nations attempt to evacuate thousands of their diplomats and civilians as well as numerous Afghans. Mothers, fathers and children have pushed up against concrete blast walls in the crush as they seek to get a flight out.

Switzerland postponed a charter flight from Kabul on Saturday because of the chaos at the airport.

Maj Gen William Taylor, with the US military’s Joint Staff, told a Pentagon briefing that 5,800 US troops were positioned at the airport and that the facility “remains secure”.

Taylor said some gates into the airport were temporarily closed and reopened over the past day to facilitate a safe influx of evacuees.

Taliban officials have tried to blame the anarchy at the airport on the US, while foreign governments have blamed the hardline Islamic group for blocking many from reaching the airport.

Speaking to an Iranian state television channel late on Saturday night in a video call, the Taliban spokesperson Mohammad Naeem also blamed the deaths at the airport on the Americans in what quickly became a combative interview.

“The Americans announced that we would take you to America with us and people gathered at Kabul airport,” Naeem said. “If it was announced right now in any country in the world, would people not go?”