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US President Donald Trump issued a stark warning to North Korea on Sunday, telling Pyongyang's leadership they "won't be around much longer".

Trump issued the threat via an early morning tweet, in response to a speech by North Korean Foreign Minister Minister Ri Yong Ho to the UN.

Yong Ho warned of an attack against the US and criticised the president calling him "deranged".

The US president responded on Twitter, ramping up the rhetoric between the two countries.

"Just heard foreign minister of North Korea speak at UN. If he echoes thoughts of Little Rocket Man, they won't be around much longer!" he said, referring to the country's leader Kim Jong Un.

Trump and Jong Un have rallied a number of insults to one another, with the US president calling North Korea's leader "Rocket Man" on a number of occasions.

Speaking to the UN, the North Korean foreign minister accused Trump of being "a mentally deranged person full of megalomania" and said that he was bringing the US closer to an attack.

"None other than Trump himself is on a suicide mission," Yong Ho told the UN General Assembly. 

"In case innocent lives of the US are harmed because of this suicide attack, Trump will be held totally responsible."

It follows a number of missile and nuclear tests by North Korea, which have tested the strong words of the US president.

On Saturday, China and South Korea said there were two earthquakes close to an area North Korea has tested nuclear weapons, sparking fears Pyongyang had detonated a new nuke.

US fighter jets and bombers held a display on Saturday, flying "the farthest north" of the Korean Peninsula in the 21st Century.

"This mission is a demonstration of US resolve and a clear message that the president has many military options to defeat any threat," the defence department said.

Trump also tweeted a warning to Iran, alleging a link between Tehran's latest missile test and North Korea.