United Nations: US President Donald Trump has raised hopes at the United Nations on Monday that a second meeting with North Korea's Kim Jong-un could occur "quite soon," striking a conciliatory tone one year after he used his debut at the UN to deride the autocrat as "Little Rocket Man" and threaten to "totally destroy North Korea" if the US were forced to defend itself or allies.

Trump praised Kim as "very open" and "terrific," despite the glacial pace of progress toward denuclearisation on the Korean Peninsula.

Donald Trump talks to Nikki Haley, the US ambassador to the United Nations, at the United Nations General Assembly on Monday in New York. Credit:AP

US officials defended Trump's strategy of engagement with the erstwhile pariah state as the president embarked on a week of meetings with world leaders. The softer tone toward North Korea - once threatened with "fire and fury" - has been replaced by rosy optimism, with Trump reserving tough rhetoric for another potential nuclear aspirant and strategic foe: Iran.

"It was a different world," Trump on said Monday of his one-time moniker for the North Korean leader. "That was a dangerous time. This is one year later, a much different time."