The Defence Secretary has said the evacuation of British nationals and former Afghan staff is "down to hours now, not weeks".
Ben Wallace said if the US extends its timetable "even by a day or two, then that will give us a day or two more to evacuate people".
"We have to make sure we exploit every minute to get people out," he said.
There are about 1,000 British troops, as well as RAF aircraft, working on getting people out of Afghanistan.
Mr Wallace said the US has provided "the framework" to allow the UK withdrawal and when the Americans leave Kabul, "we will have to go as well".
"I don't think there is any likelihood on staying on after the United States," he said.
Watch: Last week, an emotional Ben Wallace admitted 'some people won't get back' from Afghanistan.
It comes as Prime Minister Boris Johnson is expected to use an emergency G7 summit to follow up on the UK's push for US President Joe Biden to extend the Kabul evacuation deadline.
But on Sunday, the US President signalled that he did not want US forces to stay in Afghanistan beyond August.
Mr Biden also said he thought US efforts to rescue American citizens from Afghanistan could wrap up at the end of the month.
Mr Wallace, however, said "the United States and the G7 are not the only stakeholders in this".
"The Taliban now have a vote and the security situation is precarious and I think that's why we have to see what we can do," he said.
"It's in the Taliban's interest to keep the country open."