US President Donald Trump said on Monday he would be willing to meet North Korean leader Kim Jong-un "under the right circumstances" to defuse tensions over North Korea's nuclear programme.

"If it would be appropriate for me to meet him, I would absolutely, I would be honoured to do it," CNN quoted Trump as saying in an interview to Bloomberg News on Monday. "If it's under the, again, under the right circumstances. But I would do that."

No US President has ever before met the leader of North Korea, and the idea is extremely controversial.

Trump's comment comes amid rising tensions between the US and North Korea as Pyongyang has sought to advance its nuclear and ballistic missile programmes and Washington has made a show of force in the region to deter their use.

The US directed an aircraft carrier-led strike group to the region as well as deployed a new anti-ballistic missile system to South Korea.

The North Korean nuclear issue has quickly become one of the top national security concerns for the Trump administration. Trump has focused on finding a diplomatic solution to the North Korean issue -- working increasingly closely with China -- but has also refused to rule out a military solution to the problem.