New York, New York - President Donald Trump said Tuesday that US relations with Britain were better under new Prime Minister Andy Burnham, but he criticized a deal to hand over the Chagos Islands.

Trump and Burnham shook hands as they met for the first time on the sidelines of the United Nations General Assembly in New York.

"No, I think they're up – well, they're more up now than they were with your last prime minister, let me put it that way," Trump told reporters, referring to previous PM Keir Starmer, with whom he had a particularly contentious relationship.

"Right now, based on my relationship with your prime minister Andy, I think that we're doing very well."

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Labour Party leader Burnham took over from Starmer in July.

Starmer initially succeeded in charming Republican Trump, including by inviting him for a state visit hosted by King Charles III a year ago, but they fell out after Britain refused to join the US-Israeli war on Iran.

Trump added that he believed Burnham would be reconsidering a deal to return the Chagos Islands – which host the strategic Diego Garcia US-UK military base – to Mauritius.

"I don't support it, I think it's terrible," Trump said when asked about the Chagos deal.

"It's amazing how strategic it is, and I think the prime minister is going to be looking at it," Trump said, as Burnham, sitting beside him, nodded and said: "yeah."