The mission to evacuate people from Afghanistan to the UK "has to come to an end" when US troops withdraw, the armed forces minister has said.
James Heappey said the UK was working to a deadline of 31 August, when the US is set to leave – though the prime minister is expected to ask President Joe Biden for more time.
Evacuations are also dependent on Taliban co-operation, Mr Heappey added.
But he said the UK was "taking nothing for granted" with the militants.
Boris Johnson will ask Mr Biden to extend the deadline in order to allow evacuation flights to continue when they meet at an emergency gathering of world leaders from the G7 countries on Tuesday.
Mr Heappey told BBC Breakfast that 6,631 people had been evacuated in the past week, and there would be nine flights over the next 24 hours.
He said this would not be possible without the US, which "has effectively taken over the full operation" at the airport.
"If there is no opportunity to extend [the deadline] – either because there's not the international appetite to do so, or perhaps more likely the Taliban are unwilling to allow us to – then we need to continue with our plans to be out by 31 August," he said.
"If that is to be the case, every minute counts to get as many people out in the meantime."
Later, on BBC Radio 4's Today programme, he said "the period of time it would take to get in place a replacement force is not realistic".
He added that the Taliban also "gets a vote" on whether evacuations continue after August, and that "apparently they've indicated that they wouldn't be" supportive of an extension.
The Foreign Office said it had sent five additional members of staff to Kabul to help with the evacuation, bringing the total number of its staff there to 19.