The Defence Secretary has said it is "unlikely" the evacuation of Kabul will be extended past the 31 August deadline.
It comes ahead of Prime Minister Boris Johnson speaking to US President Joe Biden about the situation in Afghanistan at an emergency G7 meeting.
Ben Wallace told Sky News: "I think it is unlikely. Not only because of what the Taliban has said but if you look at the public statements of President Biden I think it is unlikely.
"It is definitely worth us all trying, and we will."
Mr Wallace said about 8,600 people have been evacuated from Afghanistan in the past fortnight, including more than 2,000 in the last 24 hours, but warned: "We're not going to get everybody out of the country."
Watch: Last week the head of the UK Armed Forces said troops are 'collaborating' with the Taliban in evacuating from Kabul.
Roughly 1,000 British troops, plus RAF aircraft, are deployed to the Afghan capital to help with the evacuation mission.
Last week, Mr Biden suggested US efforts to rescue American citizens from Afghanistan could wrap up at the end of the month.
The US military has since completed its biggest day of evacuations out of Afghanistan by far, with 28 flights taking 10,400 people out of the Taliban-controlled country over 24 hours ending early on Monday morning.
Fifteen C-17 transport aircraft flights brought out another 6,660 over the next 12 hours, White House officials said.
Chief Pentagon spokesman John Kirby said the faster pace of evacuation was due in part to co-ordination with Taliban commanders on getting evacuees into the airport.
The head of the UK Armed Forces said last week that British troops were "collaborating" with the Taliban on the ground.
However, the Taliban have now signalled they might soon seek to shut down the airlifts.
Speaking to BBC Radio 4's Today programme, Mr Wallace insisted it would not be appropriate to try to secure Kabul airport with British troops after the US pulls out.
"It's not about effectively whether I could fly in thousands of troops and secure the airport," he said.
"Yes, I could do that. I could probably secure the airport for a few months, or maybe a year or two.
"But for what purpose? For them to be shot at, attacked, people not to get to the airport and to trigger just a permanent fight? I don't think that is a solution," he added.
Mr Wallace also told Sky News that as the 31 August deadline approaches "I think it's correct to say the security risk goes up", mentioning so-called Islamic State as a potential threat.
Shadow foreign secretary Lisa Nandy has called on the Prime Minister to "step up" and "change course" after years of "trashing our alliances".
She told BBC Breakfast there is not much more soldiers, diplomats, and UK staff on the ground can do, but said there is "certainly" more that the politicians can do to support them.
Kabul airport has been the centre of chaotic scenes since the Taliban takeover, with Afghans desperately attempting to flee the country.
The Ministry of Defence said over the weekend that seven Afghan civilians were killed in a crush outside the airport.
Further details about support available can be found on the Forces News website.
Cover image: UK coalition forces, Turkish coalition forces, and US Marines assist a child during an evacuation at Kabul airport (Picture: US Department of Defense).