Donald Trump has said he has a “very good relationship” with Keir Starmer and is considering making the UK the first country he visits during his second term as president.

Speaking to reporters onboard Air Force One, Trump said he and Starmer “get along well” despite their divergent political views and that they were due to have a call this weekend.

“He’s liberal, which is a bit different from me, but I think he’s a very good person and I think he’s done a very good job thus far,” Trump told the BBC.

“He’s represented his country in terms of philosophy … I may not agree with his philosophy, but I have a very good relationship with him.”

The US president was asked about his relationship with the British prime minister after responding to a question about the location of his first international visit, which he said “could be Saudi Arabia, it could be UK. Traditionally, it could be UK.”

He said the last time he travelled to Saudi Arabia, it was because the kingdom had agreed to buy billions of dollars’ worth of US merchandise. “If that offer were right, I’d do that again,” he said.

Trump and his wife, Melania, made a state visit to the UK in 2019 and were hosted by the late queen. Ministers are open to extending another invitation, which would make Trump the first elected politician in modern history to be hosted for two state visits.

David Lammy, the foreign secretary, suggested earlier this month that Starmer would visit Washington within weeks for talks with Trump.

The pair spoke by phone after Trump’s re-election in November. Downing Street said at the time that they agreed the relationship between the UK and US was “incredibly strong” and would “continue to thrive”.

Several diplomatic challenges for the US-UK relationship are looming, however, including Trump’s pledges to introduce trade tariffs and slash support for Ukraine.

It is also unclear whether Trump will approve the UK’s proposed deal to cede sovereignty over the Chagos Islands, where there is a joint US-UK military base, to Mauritius. Efforts to finalise the deal before Trump’s inauguration were halted to give the incoming president time to examine it.

Meanwhile, questions have been raised over whether Trump will accept the nomination of Peter Mandelson, the Labour peer and architect of New Labour, as the British ambassador to Washington.

There have also been concerns within government about the attacks on Starmer by the tech billionaire Elon Musk on his social media platform, X. Musk, who has called for the prime minister to be ousted, is a key ally and donor to Trump who has been chosen to run the newly formed US Department of Government Efficiency.

Morgan McSweeney, Starmer’s chief of staff, and Jonathan Powell, his national security adviser, travelled to the US in December for talks with Trump’s White House team.

Trump’s comments came as a major poll suggested that voters favoured the UK moving closer to Europe on trade, rather than Washington. Starmer has argued that the UK does not have to choose between the US and Europe and that it is in the national interest to work with both.

In a speech last month, the prime minister said the UK would “never turn away” from its relationship with the US, despite the difficulties the new administration could pose, as it had been the “cornerstone” of security and prosperity for over a century.