The UK prime minister is expected to ask U.S. President Joe Biden to keep American forces in Afghanistan beyond the 31 August deal 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 U.S. intends to pull all troops out by the end of the month.
President Biden said the U.S. troops have 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.