The alliance between the US and the UK should be known as the "indestructible relationship", Boris Johnson has told the BBC after meeting US President Joe Biden for the first time.
He said he had "terrific" talks with Mr Biden, who has travelled to Cornwall for the G7 summit of world leaders.
The summit begins later, with vaccines and climate change on the agenda.
Mr Johnson insisted the US president had not rebuked him over post-Brexit tensions in Northern Ireland.
However, Mr Biden is said to have "deep concern" over the situation.
The prime minister was speaking to the BBC's political editor Laura Kuenssberg, after meeting Mr Biden in Carbis Bay, Cornwall, on Thursday ahead of the G7 summit.
The summit will see the leaders of Canada, France, Germany, Italy, Japan, the US and UK gathering in person for the first time since the pandemic.
Ahead of the meeting, Mr Johnson pledged the UK would donate more than 100 million vaccines to poorer countries in the next year, while Mr Biden promised 500 million doses of Pfizer vaccines to 92 low and middle-income countries and the African Union.
The G7 nations are expected to collectively agree to provide a billion doses of Covid-19 vaccine in an effort to end the pandemic in 2022.
Mr Johnson told the BBC the UK and US shared a belief in human rights, the rules-based international order and the transatlantic alliance.
He said he thought of the association as "an indestructible relationship" or the "deep and meaningful relationship".
"It's a relationship that has endured for a very long time, and has been an important part of peace and prosperity both in Europe and around the world," he said.
The PM had previously let it be known that he preferred a new term for the so-called "special relationship" between the UK and US after decades of use.