Donald Trump said he would "be honoured" to meet with brutal North Korean dictator Kim Jong-un amid heightened tensions over the rogue regime's nuclear weapons program.

"If it would be appropriate for me to meet with him, I would absolutely, I would be honoured to do it," President Trump said in an interview with Bloomberg News. "If it's under the, again, under the right circumstances. But I would do that."

North Korea has become the most urgent national security threat and foreign policy issue facing Trump, with US Secretary of State last week hinting North Korea could be added to the state sponsor of terrorism list.

"Most political people would never say that," Trump said of his willingness to meet with the reclusive Kim, "but I'm telling you under the right circumstances I would meet with him. We have breaking news."

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The US president's comments come a day after North Korea test-launched a short-range ballistic missile, in defiance of UN sanctions and international condemnation.

The North Korean leader - who has had his own family members executed by flamethrowers and anti-aircraft weapons - has never met with a foreign leader since taking charge after his father's death in 2011 and hasn't left his isolated country.

Donald Trump called North Korean leader Kim Jong-un a
Donald Trump called North Korean leader Kim Jong-un a "pretty smart cookie". Photo / AP