Crowds have grown at the airport in the heat and dust of the day over the last week, with mothers, fathers and children pushed up against concrete blast walls in the crush as they seek to get a flight out. 

The Taliban have urged those without travel documents to go home. At least 12 people have been killed in and around the single runway airfield since Sunday, NATO and Taliban officials said. 

"Because of potential security threats outside the gates at the Kabul airport, we are advising U.S. citizens to avoid travelling to the airport and to avoid airport gates at this time unless you receive individual instructions from a U.S. government representative to do so," a U.S. Embassy advisory said. 

The German Embassy also advised its local citizens not to go to the airport, warning in an email that the Taliban were conducting increasingly strict controls around the airport. 

A senior U.S. military official said there had been short periods in the last 24 hours when the gates to Kabul airport have been closed, but no reported change in the "enemy" situation in and around the single-runway airfield. 

A Taliban official, speaking to Reuters, said security risks could not be ruled out but that the group was "aiming to improve the situation and provide a smooth exit" for people trying to leave over the weekend. 

The Taliban are still trying to hammer out a new government and the group's co-founder, Mullah Baradar, arrived in Kabul for talks with other leaders on Saturday. 

The group's lightning advance across the country as U.S.-led forces pulled out, coinciding with what German Chancellor Angela Merkel described on Saturday as the "breathtaking collapse" of the Afghan army, sparked fear of reprisals and a return to a harsh version of Islamic law the Taliban exercised when they were in power two decades ago. 

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

"The security situation around Kabul airport has worsened significantly in the last hours. A large number of people in front of the airport and sometimes violent confrontations are hindering access to the airport," the Swiss Federal Department of Foreign Affairs said in a statement on Saturday. 

The United States had evacuated 2,500 Americans from Kabul over the past week, senior U.S. officials said on Saturday, adding that Washington was fighting against "time and space" to evacuate people from Afghanistan. 

Army Major General William Taylor, with the U.S. military's Joint Staff, told a Pentagon briefing that 3,800 people had been evacuated on U.S. military and chartered flights from Kabul in the past 24 hours, bringing to 17,000 the total number of people evacuated in the current mission. 

Pentagon spokesman John Kirby said he did not have a "perfect figure" on how many Americans remain in the country. 

The Taliban official said the group planned to ready a new model for governing Afghanistan within the next few weeks, with separate teams to tackle internal security and financial issues. 

"Experts from the former government will be brought in for crisis management," he told Reuters. 

The new government structure would not be a democracy by Western definitions, but "it will protect everyone's rights", the official added. 

Baradar will meet militant commanders, former government leaders and policy makers, as well as religious scholars among others, the official said. 

The delay in forming a new government or even announcing who will lead a new Taliban administration underlines how unprepared the movement was for the sudden collapse of the Western-trained forces it had been fighting for years. 

The Taliban, whose overall leader Mullah Haibatullah Akhundzada has so far been silent publicly, must also unite disparate groups within the movement whose interests may not always coincide now that victory has been achieved. 

The Taliban follow an ultra-hardline version of Sunni Islam. They have sought to present a more moderate face since returning to power, saying they want peace and will respect the rights of women within the framework of Islamic law. 

When in power from 1996-2001, also guided by Islamic law, they stopped women from working or going out without wearing an all-enveloping burqa and stopped girls from going to school. 

Individual Afghans and international aid and advocacy groups have reported harsh retaliation against protests, and round-ups of those who had formerly held government positions, criticised the Taliban or worked with Americans. 

"We have heard of some cases of atrocities and crimes against civilians," said the Taliban official on condition of anonymity. 

"If (members of the Taliban) are doing these law and order problems, they will be investigated," he said.