US President Donald Trump has accepted an invitation to meet North Korean leader Kim Jong Un, an extraordinary development following months of heightened nuclear tension and frequent threats and insults, media reports said.

The news was confirmed on Thursday night by both the White House and visiting South Korean National Security Adviser Chung Eui-yong.

"President Trump greatly appreciates the nice words of the South Korean delegation and President Moon. He will accept the invitation to meet with Kim Jong Un at a place and time to be determined. We look forward to the denuclearisation of North Korea. In the meantime, all sanctions and maximum pressure must remain," CNN quoted White House press secretary Sarah Sanders as saying.

After meeting Trump at the White House, Chung said: "He (Kim) expressed his eagerness to meet President Trump as soon as possible.

"President Trump said he would meet Kim Jong Un by May."

Chung however, did not provide any information on where the meeting would take, reports The Washington Post.

Chung led the South Korean delegation earlier this week to North Korea, where Kim and his senior cadre expressed a willingness to hold talks with the US and were prepared to discuss denuclearisation and normalising relations.

In Seoul, the presidential Blue House clarified that the meeting would occur by the end of May.

Trump also expressed his optimism about the meeting in a post on Twitter, saying that Kim had "talked about denuclearisation with the South Korean Representatives, not just a freeze", The New York Times reported.

"Also, no missile testing by North Korea during this period of time... Great progress being made but sanctions will remain until an agreement is reached. Meeting being planned!"

Trump and Kim have spent the past year making belligerent statements about each other, with Trump mocking Kim as "Little Rocket Man" and pledging to "totally destroy" North Korea and Kim calling the ­American ­President a "dotard" and a "lunatic" and threatening to send nuclear bombs to Washington, D.C.

No sitting American President has ever met a North Korean leader, The Washington Post reported.

Former president Jimmy Carter met Kim's grandfather Kim Il-sung, and former president Bill Clinton met his father, Kim Jong-il - during visits to Pyongyang after they had left office.

Both Carter and Clinton also went to Pyongyang to collect Americans who had been imprisoned by the regime.

Since he took over the leadership of North Korea from his father at the end of 2011, Kim Jong Un has not met any other head of state.

Discussions were now underway to hold a summit with South Korean President Moon Jae-in in the demilitarised zone between the two Koreas at the end of next month.

After a year in which North Korea fired intercontinental ballistic missiles capable of reaching all of the US and tested what is widely thought to have been a hydrogen bomb, such a moratorium would be welcomed by Washington and the world.