The UK's Afghanistan evacuation operation is "down to hours now, not weeks", Defence Minister Ben Wallace has said.
US President Joe Biden has said his government was discussing the possibility of extending the deadline to leave Afghanistan beyond August 31, but hoped it would not be necessary.
The US will consider an extension if asked to do so by G7 allies, but was working closely with those countries and others to help them repatriate their citizens, he said.
On Tuesday, UK Prime Minister Boris Johnson is set to discuss the crisis with the EU and leaders of fellow G7 member states, the US, Italy, France, Germany, Canada and Japan.
Mr Johnson is "going to try and raise the prospect of seeing if the United States will extend", Mr Wallace said.
"It's really important for people to understand the US have over 6,000 people in Kabul airport and when they withdraw that will take away the framework, and we will have to go as well," he said.
"I don't think there is any likelihood of staying on after the US. If their timetable extends even by a day or two, that will give us a day or two more to evacuate people.
"Because we are really down to hours now, not weeks, and we have to make sure we exploit every minute to get people out."
But the Taliban said there would be consequences if foreign forces did not leave Afghanistan before the end of the month.
Mr Johnson's spokesman said the government had not set a "hard deadline" for when the evacuation operation would end.
He dismissed suggestions that the prime minister at the G7 summit would push for more sanctions against the Taliban, despite a Reuters report suggesting otherwise.
Sanctions against the Taliban are unlikely to be adopted immediately, a western diplomat said.
Mr Johnson and Mr Biden agreed on Tuesday to work together to ensure all those eligible to leave Afghanistan were able to, including after the initial evacuation phase ended, Downing Street said.
"They discussed the ongoing efforts by the UK and US to co-ordinate the rapid and safe evacuation of our nationals, and those who previously worked with our governments, from Kabul International Airport," a spokesman said.
"The leaders agreed to continue working together to ensure those who are eligible to leave are able to, including after the initial phase of the evacuation has ended."
The two leaders also noted the importance of concerted diplomatic engagement to secure the progress made in Afghanistan and prevent a humanitarian crisis, Mr Johnson's office said.
"They committed to driving international action, including through the G7 and UN Security Council, to stabilise the situation, support the Afghan people and work towards an inclusive and representative Afghan government," the spokesman said.
On Sunday, Mr Biden said the Taliban had not attacked US troops in control of Kabul airport, and had largely lived up to their pledge to let American citizens reach the site safely.
Taliban fighters seized control of Kabul last weekend, forcing civilians and foreigners to flee.
Many fear a return to the strict interpretation of Islamic law imposed by the Taliban during their previous rule, which ended 20 years ago.
Two UK ministers have said Britain wants the evacuation deadline to be extended.
James Heappey, Minister for the Armed Forces, said about 4,000 people who were eligible to enter the UK were still in Afghanistan.
The government wants to rescue thousands more if it can, Mr Heappey said.
James Cleverly, Minister of State for Middle East and North Africa, said an extension would allow western countries to bring more people out of Afghanistan.
“The more time that we've got, the more people we can evacuate – and that’s what we're pushing for," he told the BBC.
“So we are prioritising getting as many people out as quickly as possible. If we can buy more time that is great, but I think that we shouldn’t be relying on the fact that we will get more time to do this.”
Scotland's First Minister Nicola Sturgeon, meanwhile, has issued a warning against a “cut-and-run operation” in Afghanistan.
Ms Sturgeon said she was not yet sure how many Afghan refugees her country would take in.
On Sunday, Mr Johnson tweeted that it was important for the international community to work together to "ensure safe evacuations, prevent a humanitarian crisis and support the Afghan people to secure the gains of the last 20 years".
UK Foreign Secretary Dominic Raab first raised the possibility of imposing sanctions to put pressure on the Taliban last week.
Mr Biden is facing criticism at home and abroad over his handling of the withdrawal of US forces.
He said last week that G7 leaders would work out a joint approach to the Taliban.
Mr Biden has already held talks with Mr Johnson, German Chancellor Angela Merkel, French President Emmanuel Macron and Italian Prime Minister Mario Draghi.
The UK will accelerate the removal of British and Afghan citizens from Afghanistan on Monday. It plans to fly up to 6,000 people from Kabul this week.
But military evacuation flights cannot go directly to civilian airports from Afghanistan, and evacuees are being sent to military transit points in the region and beyond.
On Monday, French Foreign Minister Jean Yves Le Drian visited the UAE, which is hosting civilians fleeing the country, including French citizens and Afghans.
The deadline for the last Royal Air Force evacuation flight has been extended from Tuesday to either Friday or Saturday.
Britain has flown out more than 5,700 people from Afghanistan since August 13, the Ministry of Defence said on Sunday.
Russia’s President Vladimir Putin has criticised western countries seeking to temporarily move Afghan refugees to Central Asia.
Mr Putin said Moscow did not “want militants appearing [in Russia] again under the guise of refugees”.
Earlier on Sunday, the Pentagon said it ordered commercial airlines to aid evacuation efforts by providing aircraft for people who had been flown from Kabul to US bases overseas.
Mr Biden said on Friday that he and US Secretary of State Antony Blinken would work with other countries to set “harsh conditions” for any co-operation with or recognition of the Taliban, based on their treatment of women and girls, and the group's overall human rights record.