Relations between the US and the UK are “more up” now that Andy Burnham is Prime Minister than when Sir Keir Starmer held the role, Donald Trump has claimed.

The US president made the remarks following his first face-to-face meeting with Mr Burnham on the sidelines of the United Nations General Assembly in New York.

Mr Burnham claimed he had “established a good connection” with Mr Trump, adding that the pair had “taken that further today” as they discussed trade, energy and immigration among other topics during their 40-minute meeting.

In his UN debut, the Prime Minister also stressed that Britain has a “positive story” to tell about itself, in an attempt to draw a line under 10 years of post-Brexit turbulence.

But despite the warm words, there are differences between the two leaders over issues including the regulation of artificial intelligence and the plan to hand over sovereignty of the Chagos Islands, including the strategic UK-US Diego Garcia military base.

As he took questions from reporters, Mr Trump disagreed that relations between America and Britain had become strained, telling them: “No, I think they are up.”

He added: “They are more up now than they were with your last prime minister, let me put it that way.”

Relations between Mr Trump and Sir Keir grew increasingly strained earlier this year when the former prime minister refused to involve Britain in the US war with Iran.

The president praised Mr Burnham as a “natural business person” based on their exchanges over the phone.

He added: “I think right now, based on my relationship with your Prime Minister, Andy, I think we’re doing very well.”

Mr Burnham said he and the president had “established a good connection in our early discussions and we’ve taken that further today”.

He joked about Mr Trump referring to Manchester as a “town” when the US president was first asked about Mr Burnham’s rise to power.

“I don’t hold it against you as the former mayor,” Mr Burnham said.

The US president opened the meeting by praising the Prime Minister’s “great election win” in the Makerfield by-election.

He continued: “That was a big one, and I think he’s going to be a great prime minister. I think he’s got a lot of assets on his side.

“And we talked about everything from Rolls-Royce to energy to immigration – we covered a lot.”

Mr Trump added: “It’s a really special country and we are with you all the way, Mr Prime Minister.”

Mr Burnham also appeared to counter narratives around Britain and other European nations falling into decline, an idea which has become a talking point among high-profile figures in the Trump administration.

He told reporters he had been “explaining to the president” that Britain has “been in too much turbulence”, and that he had shared his vision for a decade of turning around the country’s fortunes.

Sitting alongside the US leader, Mr Burnham added: “I think you responded when I said we are going to lay out a plan for Britain, a 10-year direction.

“The country’s got so much going for it, and it’s time to turn the story about Britain to a positive story, get some hopefulness going around the country, and I think you were saying today that very much is how you see it.”

“Right,” Mr Trump responded.

Elsewhere during their meeting, the US President criticised Britain’s handling of the Chagos Islands deal, which he described as a “very important piece of real estate, militarily and strategically” for both the UK and America.

A joint US-UK military base is located on the largest of the islands, Diego Garcia, which Britain would lease from Mauritius under the £3.4 billion deal.

Mr Trump branded the agreement to hand sovereignty of the Indian Ocean islands to Mauritius as a “terrible deal”, and suggested that the Prime Minister was “going to be looking at it”.

The pair earlier appeared at odds over the future of AI, with Mr Burnham calling for internationally-agreed regulation of the technology, while the President said the US would reject any such “globalist scheme”.