The UK prime minister is expected to ask US President Joe Biden to keep American forces in Afghanistan beyond 31 August in order to allow evacuation flights to continue.
Boris Johnson will make the request at an emergency meeting of world leaders from the G7 countries on Tuesday.
Many thousands of people are crowded outside Kabul airport, desperate to leave after the Taliban swept to power.
The US intends to pull all troops out by the end of the month.
Mr Biden said discussions were taking place about extending the deadline, but that “our hope is we will not have to”.
He said US troops had expanded the perimeter around Hamid Karzai International Airport as part of efforts to speed up evacuation efforts, and the Taliban had cooperated with the move.
While UK government officials have said there is “no fixed date” for UK withdrawal, it is feared that without US troops on the ground the remaining allied forces will be unable to secure the area.
The UK has more than 1,000 Armed Forces personnel deployed in Kabul.
