He said he had “fabulous” talks with Biden, who has traveled to Cornwall for the G7 world leaders summit.
Johnson insisted the US president had not reprimanded him for post-Brexit tensions in Northern Ireland.
However, Biden is said to have “deep concern” about the situation.
The two men met in Carbis Bay, Cornwall on Thursday before the start of the G7 summit, which will see the leaders of Canada, the EU, France, Germany, Italy, Japan, the United States and the United Kingdom meet in person by first time. since the pandemic.
Before the meeting, Johnson promised that the UK would donate more than 100 million vaccines to the poorest countries next year, while Biden promised 500 million doses of Pfizer vaccines to 92 low- and middle-income countries and the African Union.
In an interview political editor Laura Kuenssberg, Johnson said the UK and the US shared a belief in human rights, the rules-based international order and the transatlantic alliance.
He said that he thought of association as “an indestructible relationship” or the “deep and meaningful relationship”.
“It is a relationship that has endured for a long time and has been an important part of peace and prosperity both in Europe and around the world,” he said.
The prime minister had previously made it known that he preferred a new term for the so-called “special relationship” between the United Kingdom and the United States after decades of use.
One area that could cause friction between the two men is the Northern Ireland Protocol, the part of the Brexit deal that prevents checks along the Irish border.
Biden previously warned that the new agreements should not jeopardize the Good Friday Agreement, a peace agreement signed in 1998 that helped end decades of violence in Northern Ireland.
When asked if Biden had voiced his concerns, Johnson said, “No, the president didn’t say anything of the sort.”
The prime minister suggested that the way the EU was implementing the agreed deal was “excessively burdensome” and said that while the UK, the US and the EU wanted to preserve the balance in Northern Ireland, it was unlikely. that a solution to the problem will be found in the next few days.
However, he added that the different parties could “figure it out.”
The deals were laid out in the 2019 Brexit withdrawal agreement, but the UK has since sought more flexibility.
On Thursday, European Commission President Ursula von der Leyen said the protocol was the “only solution” and that it should be fully implemented.
And French President Emmanuel Macron said: “I think it is not serious to want to review in July what we finalized after years of debate and work in December.
“We have a trade agreement, it has been painfully debated for years … if six months later, they say: ‘What we negotiate with you, we don’t know how to respect it,’ then that means that nothing is respectable anymore. ”
Johnson also defended his decision to cut spending on foreign aid from 0.7% to 0.5% of national income, despite a manifesto promise to maintain the highest level.
Earlier in the week, Johnson faced strong criticism from some of his own MPs, one of whom said the cuts would lead to “hundreds of thousands of preventable deaths.”
The prime minister said his government aid spending as a percentage of GDP exceeded the amount spent by the last two Labor prime ministers.
She argued that the public understood the financial strain caused by the pandemic, adding: “I believe that the people in this country, despite the constant exhaustion of this country’s efforts, are incredibly proud of what we are doing despite the hardships. that we face. versus.”
He also noted the UK’s commitment to donate 100 million doses of surplus vaccines to the poorest countries next year, as well as previous doses contributed to Covax, the plan that distributes vaccines to the world’s poorest nations.
“We will have a colossal sum of vaccines that we will distribute; the fight against Covid would not be possible without the UK’s efforts on vaccines,” he said.
Johnson also said that he had discussed the Harry Dunn case with the US president and that Biden was “extremely understanding” and “actively involved” in the case.
The G7 brings together seven leading industrialized countries.
They will spend the day discussing topics like the pandemic before a lavish reception attended by the Queen.
The Duke and Duchess of Cambridge will also participate in their first G7 events.
William and Kate will join the Queen, the Prince of Wales and the Duchess of Cornwall at the G7 leaders’ reception.
Afterwards, Prince Charles will host a reception for G7 leaders and heads of the world’s largest companies to discuss how the private sector can work with governments to address the climate emergency.