President Trump has said he would be "honoured" to meet North Korea's Kim Jong-Un "under the right circumstances".
"If it would be appropriate for me to meet with him, I would, absolutely, I would be honoured to do it," he told Bloomberg News.
Tensions between the US and North Korea are reaching boiling point amid fears the secretive state could follow up recent missile launches with a nuclear test.
The President has refused to rule out a pre-emptive strike, but has also been trying to get China to convince the North Korean leader to stop the tests.
:: Donald Trump plays 'good cop' with China over North Korea
Mr Kim's regime has threatened devastating retribution should the US try to attack, including sinking its huge USS Carl Vinson aircraft carrier.
Mr Trump told Bloomberg that "most political people would never say" they would meet Kim, adding: "I'm telling you, under the right circumstances, I would meet with him. We have breaking news."
White House press secretary Sean Spicer later said any such meeting would have to follow a significant change of behaviour by North Korea.
"Clearly conditions are not there right now," he added.
In a separate interview at the weekend with CBS, President Trump said he would "see" about military action - but also referred to Kim Jong-Un as a "smart cookie".
"A lot of people, I'm sure, tried to take that power away, whether it was his uncle or anybody else," said President Trump.
"And he was able to do it. So obviously, he's a pretty smart cookie. But... we cannot let what's been going on for a long period of years continue."
"People are saying, 'Is he sane?' I have no idea," added the President.
North Korea recently paraded its military hardware, including large rockets, through the centre of the capital Pyongyang in an elaborate display.
However, its last three rocket tests have ended in failure.
US officials said a medium-range KN-17 missile, launched last week, appeared to have broken up within minutes and did not leave North Korean territory.
President Trump framed the test as a snub to China - the North's largest trading partner - and tweeted: "North Korea disrespected the wishes of China & its highly respected President when it launched, though unsuccessfully, a missile today. Bad!"
US Secretary of State Rex Tillerson told the UN last week that it was a "matter of time" before North Korea develops a nuclear weapon that can hit the American mainland.
But the world's most secretive country has refused to abandon its nuclear programme.
The deputy ambassador to the UN, Kim In Ryong, hit back at Mr Tillerson and insisted its nuclear weapons would never be part of "political bargains and economic deals".
"In a nutshell, DPRK have already declared not to attend any type of talks which would discuss its nuclear abandonment, nuclear disbandment," he said.