Trump expresses optimism on US-Iran deal during UN meeting with British PM Andy Burnham

"I think that a settlement is going to be reached," Trump said after a meeting with British Prime Minister Andy Burnham on the sidelines of the UN General Assembly in New York.

US President Donald Trump said that Iran and the United States had been talking on Tuesday, and he thinks the two countries will reach a deal at some point.

Trump also told reporters that US officials, including Steve Witkoff and Jared Kushner, had had a "very good" three-hour meeting on Tuesday with the Iranian delegation.

"I think that a settlement is going to be reached," Trump said after a meeting with British Prime Minister Andy Burnham on the sidelines of the UN General Assembly in New York.

"They want to talk to us. They have been talking to us; even today they've been talking to us, and the relationship is developing," he added. "But we can't let them - and they understand that - we can't let them have a nuclear weapon."

British Prime Minister Andy Burnham said on Tuesday he and US President Donald Trump had "established a good connection in our early discussions" despite their differences on some foreign policy issues as they met for the first time in New York.

Trump called Burnham a "natural business person" after their meeting where they discussed issues, including Ukraine, the status of the Falkland Islands and trade issues.

UK-US relationship a major foreign policy challenge for Burnham

"This relationship matters so much to us, and we'll build on that," Burnham said.

One of the biggest foreign policy challenges facing Burnham will be managing Britain's relationship with the United States, but he and his officials are likely to be relieved that their first public meeting passed off smoothly.

Long regarded as one of the world's closest alliances, the partnership has been strained by Trump's foreign policy agenda, including the US-Israeli decision to attack Iran this year.

After their meeting, Trump again criticized Britain's plan to resolve the status of a US-British military base on the Indian Ocean island of Diego Garcia, calling it a "terrible deal."

Burnham has pledged to find a solution.

Britain last year agreed a deal to cede sovereignty of the Chagos Islands to Mauritius after more than two centuries of control, while retaining a 99-year lease over its biggest island, Diego Garcia, and its strategic military base.

But the legislation required to implement the agreement was paused because of opposition from the United States.

"I don’t support it. It was a terrible deal," Trump said on Tuesday. "Somebody has ownership that never showed up before, after decades and centuries. I think it’s ridiculous."