Kim Jong Un is said to be open to "frank" talks with the US
Donald Trump has said he believes North Korea's offer to discuss nuclear disarmament is "sincere."
Kim Jong Un is willing to give up nuclear weapons if the security of his regime is guaranteed, according to South Korea, after he reportedly said it was the last wish of his father.
An envoy from Seoul made the announcement after meeting the North Korean leader, who is also said to be open to "frank" talks with the US.
Speaking at a White House press conference, President Trump said: "I believe they are sincere. I hope they are sincere.
"I think they are sincere also because of the sanctions and what we're doing with respect to North Korea.
"(China) can do more but I think they've done more than they have ever done for our country before."
South Korea national security adviser, Chung Eui-yong, said North Korea had "made clear its willingness for the denuclearisation of the Korean peninsula."
"Chairman Kim said that even denuclearisation could be among the agenda items for talks between North Korea and the US," a South Korean official said.
Kim Jong Un "made clear that achieving denuclearisation is his father's dying wish and that it has not been changed at all," according to the official - who was speaking anonymously.
Responding to the development, Mr Trump tweeted: "Possible progress being made in talks with North Korea.
"For the first time in many years, a serious effort is being made by all parties concerned. The World is watching and waiting! May be false hope, but the US is ready to go hard in either direction!"
Possible progress being made in talks with North Korea. For the first time in many years, a serious effort is being made by all parties concerned. The World is watching and waiting! May be false hope, but the U.S. is ready to go hard in either direction!— Donald J. Trump (@realDonaldTrump) March 6, 2018
The US has long insisted that concrete steps are taken towards denuclearisation before any discussions can take place.
North Korea's nuclear tests have sparked threats of war and insults between Kim Jong Un and Donald Trump, and the ramping up of sanctions against the secretive regime.
Its last rocket test was in November.
South Korea said the North had promised not to hold any further tests during any future talks with the US.
China welcomed the signals coming from Pyongyang and urged "all relevant parties" to "seize the current opportunity," adding that it was "willing to continue to play its due role."
The two Koreas also announced they would set up a leader-to-leader hotline and hold a summit next month at their heavily armed border.