The Prime Minister was expected to press US President Joe Biden to keep his forces on the ground past 31 August, as they are providing security at Kabul airport to allow people to flee the country.
But following an emergency meeting of G7 leaders, chaired by the PM on Tuesday afternoon, Mr Biden said the deadline remained in place.
Watch: UK personnel on their experiences of Operation Pitting, the evacuation mission in Afghanistan.
Mr Johnson said: "We will go right up until the last minute that we can but you've heard what the President of the United States has said, you've heard what the Taliban have said."
He added: "We're confident we can get thousands more out, but the situation at the airport is not getting any better."
He said leaders had agreed the "number one condition" after 31 August was that the Taliban must grant "safe passage for those who want to come out".
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Cover image: US service member at Kabul airport where evacuations are taking place (Picture: US Department of Defense).