US President Donald Trump has warned leaders gathered at the UN General Assembly that the United States may have to destroy North Korea if Kim Jong-un's nuclear-armed regime threatens its neighbours.

In his first address to the assembly, Mr Trump said: "The United States has great strength and patience, but if it is forced to defend itself or its allies, we will have no choice but to totally destroy North Korea.

"Rocket Man is on a suicide mission for himself and for his regime," he said, using his new nickname for the North Korean leader. "The United States is ready, willing, and able, but hopefully this will not be necessary."

He urged UN member states to turn up the pressure on North Korea to give up its nuclear weapons, using his maiden speech to the world body to address what he has said is the top global challenge.

Beginning his speech shortly after arriving at UN headquarters in New York, Mr Trump said the world faces destructive threats from rogue states and "terrorists and extremists".

"Rogue regimes not only support terrorists but threaten other nations with the most destructive weapon known to humanity," Mr Trump said, referring to nuclear weapons.

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It was his first appearance in the green-marbled UN General Assembly hall, where applause from world leaders is generally muted.

Reading carefully from a script, Mr Trump promised the United States military would soon be the strongest it has ever been.

Mr Trump, who came to power promoting an America First agenda, told world leaders that the US does not seek to impose its will on other nations and will respect other countries' sovereignty.

"I will defend America's interests above all else," he said. "But in fulfilling our obligations to other nations we also realise it's in everyone's interest to seek a future where all nations can be sovereign, prosperous and secure."