Wallace has said the UK will leave Kabul airport at the same time as US forces.
Speaking to media on Monday, he confirmed Prime Minister Boris Johnson will “try and seek” a US extension beyond the current 31 August evacuation deadline date at a G7 meeting tomorrow.
“When they withdraw that will take away the framework… we will have to go as well,” he said. “I don’t think there is any likelihood of staying on after the United States.”
He added that we are “really down to hours now, not weeks”, adding: “We have to make sure we exploit every minute to get people out.”
However, a spokesperson for the Taliban, Muhammad Suhail Shaheen, spoken to the BBC amid reports the UK will press for a deadline extension for international evacuations beyond 31 August.
“Foreign forces should withdraw on the deadline they have announced earlier. Otherwise, it is a clear violation,” Mr Shaheen said.
The spokesman added the Taliban’s reaction to such a move would be a decision for the group’s leadership.
Thousands of Afghans are continuing to try and flee the country ahead of the end-of-the-month deadline, with many citing fear of life under Taliban rule.
It is unclear whether international flights will be allowed in and out of the country once international forces leave and cease control of the airport.
The World Health Organization (WHO) warned Monday that more than 500 tonnes of medical supplies due for delivery in Afghanistan are stuck outside of the country due to chaos at Kabul airport.
Aid officials say the supplies, including surgical equipment and malnutrition kits, are needed to help hundreds of thousands of people displaced by recent violence.
Thousands of people have left the country in recent days, but commercial flights have ceased.
“While the eyes of the world now are on the people being evacuated and the planes leaving, we need to get supplies in to help those who are left behind,” WHO spokeswoman Inas Hamam said in a statement to Reuters.
The UN health organisation wants empty planes to divert to Dubai to pick up supplies on their way to pick up refugees.