US President Joe Biden says the US is “on pace” to meet a 31 August deadline for evacuations, despite previous calls from allies for an extension.
“The sooner we finish the better,” he said. Some American troops have already been withdrawn, US media report – although evacuations are not affected.
At least 70,700 people have been airlifted from Kabul, which fell to the Taliban nine days ago.
The militants have opposed any extension to the evacuation deadline.
President Biden said: “The Taliban have been taking steps to help get our people out,” adding that the international community would judge the Taliban by their actions.
“None of us are going to take the Taliban’s word for it,” he added.
Mr Biden said the airlift had to come to end soon because of an increasing threat from the Islamic State group in Afghanistan.
The longer the US stayed in the country, he said, there was an “acute and growing risk of an attack” by the group.
Mr Biden was speaking after leaders of the G7 – which consists of Canada, France, Germany, Italy, Japan, the UK and the US, plus the EU – discussed the Afghan crisis during a virtual meeting. The UK and other allies had urged the US to stay beyond 31 August to allow more relief fights.
UK Prime Minister Boris Johnson, who chaired the talks, said Britain would continue to evacuate people “until the last moment”. He also urged the Taliban to allow Afghans to leave beyond the deadline.
European Commission President Ursula von der Leyen said the G7 leaders had “agreed that it is our moral duty to help the Afghan people and to provide as much possible support as conditions will allow”.
Almost 6,000 US soldiers and more than 1,000 from the UK are at Kabul airport to secure it and organise the evacuation of foreigners and eligible Afghans.
Smaller contingents from other Nato members including France, Germany and Turkey are also present.
The airlift is being stepped up, with more than 21,000 people evacuated since Sunday. The departure of some US troops ahead of the 31 August deadline “does not affect the mission”, a US defence official was quoted as saying by CNN.
Earlier on Tuesday, Taliban spokesman Zabihullah Mujahid said the group would probably not agree to an extension and Afghans would be stopped from going to the airport.
“There is danger that people will lose their life” in the chaos there, he told reporters.
However, there has been confusion about whether this meant Afghans with full travel documents would be unable to leave the country.
Mr Mujahid also said that working women in Afghanistan must stay at home until proper systems are in place to ensure their safety.
“Our security forces are not trained [in] how to deal with women – how to speak to women [for] some of them,” he said. “Until we have full security in place… we ask women to stay home.”
The Taliban enforced a strict version of Islamic law when they ran Afghanistan before 2001. Since their return to power, they have tried to convey a more restrained image, promising rights for women and girls and some freedom of speech.
But UN Human Rights Commissioner Michelle Bachelet said there were “credible” reports of human rights abuses by the Taliban, including summary execution, restrictions on women and recruitment of child-soldiers.
The UN Human Rights Council on Tuesday endorsed a resolution affirming its “unwavering commitment” to the rights of women and girls.
But the resolution did not recommend the appointment of a special UN investigator for Afghanistan, which many human rights groups had called for.