Speaking to the BBC, Ben Wallace said he has "just authorised another company" to deploy to Kabul.
Mr Wallace also said "if the US stay", it provides the chance to continue evacuating British nationals and former Afghan staff from Kabul, Afghanistan's capital.
"They're doing everything from the control tower to the firefighters, they are running that airport," he said.
"I've always said our scheme is open-ended and we're never going to close that scheme.
"So long, long after we are gone, whenever that is, we are starting to invest in third-country hubs already, so we can process people if they get out to other countries in the region."
US President Joe Biden suggested his troops would stay in Afghanistan until the evacuation of Americans is complete – even if that runs past the 31 August withdrawal deadline.
Nine hundred British personnel are currently deployed on Operation Pitting, the UK's military operation getting people out of Afghanistan.
Watch: Afghanistan – 'Taliban will butcher' Afghan staff left in country, former interpreter says.
On 16 August, the UK increased its initial military support for the evacuation – including an additional 200 troops being sent to Kabul.
Earlier this week, the Chief of the Defence Staff said British forces were "collaborating" with the Taliban to get people out of Afghanistan.
The UK's Ambassador to Afghanistan also said the "speed and pace" of the operation to evacuate people from Afghanistan was set to be scaled up over the next few days.
And Royal Navy Vice Admiral Sir Ben Key, the lead for Operation Pitting, said the UK "can't afford to pause" as they continue to bring people out of Afghanistan.
It comes after former Afghan interpreters and military veterans demonstrated outside Parliament on Wednesday, calling for the support and protection of interpreters and their families still in Afghanistan.
Further details about support available can be found on our website.
Cover image: US Marines.