"What I want to assure people is that our political and diplomatic efforts to find a solution for Afghanistan -- working with the Taliban, of course, if necessary -- will go on," Johnson told reporters.
He said the situation at the Kabul airport, where thousands of Afghans gathered in hopes of boarding an evacuation flight, was getting "slightly better," and he saw "stabilization."
An Unwanted New Civil War Is What Afghans Foresee
Since Thursday, the prime minister said, Britain has been able to evacuate about 2,000 people, including British nationals and Afghans who worked with Britain.
Earlier this week, Britain's Home Office introduced a "bespoke" resettlement plan, promising to take in up to 20,000 Afghans "in the long-term," with some 5,000 being in the first year.
British lawmakers who met for an emergency parliament session on Wednesday considered the plan far from enough to deal with the Afghan crisis.
Leaders of the Group of Seven (G7) will meet online early next week to discuss the situation in Afghanistan, as the rift between Washington and its European allies seemed to have widened over the former's hasty withdrawal from Afghanistan.
On Tuesday, French daily Le Monde said, "Europeans were trapped in hasty American withdrawal." Last Friday, British Secretary of Defense Ben Wallace said that the U.S. decision to pull its military forces out of Afghanistan was a "mistake."