The US president's statement sparks new concern as Pyongyang has suggested it would continue its nuclear and missile programme.
US President Donald Trump on Monday opened the door to meeting North Korea's leader Kim Jong-un, saying he would be honoured to meet the young leader under the right circumstances.
The statement comes even as Pyongyang suggested it would continue its nuclear weapons tests.
"If it would be appropriate for me to meet with him, I would absolutely, I would be honoured to do it," Trump told Bloomberg News, drawing criticism in Washington.
"Under the right circumstances I would meet with him," Trump said.
TRT World's Iolo ap Dafydd is following the developments in Washington DC.
Trump did not say what conditions would need to be met for any such meeting to occur or when it could happen.
But, the White House later said North Korea would need to meet many conditions before a meeting could be contemplated.
"Clearly conditions are not there right now," White House spokesman Sean Spicer said.
"I don't see this happening anytime soon," Spicer added.
Trump, who took office in January, had said during his presidential campaign he would be willing to meet with Kim.
His administration has since said North Korea must agree to abandon its nuclear and missile programs.
They also sought to pressure Pyongyang economically and diplomatically while insisting that military options remain "on the table."
On Friday, US Secretary of State Rex Tillerson told the United Nations Security Council that Washington would not negotiate with North Korea.
US Vice President Mike Pence, earlier on Monday, said Trump had made clear "that the era of strategic patience is over."
Later on Monday, a US State Department spokeswoman said in a statement: "The United States remains open to credible talks on the denuclearisation of the Korean peninsula."
"However, conditions must change before there is any scope for talks to resume," she said, adding that North Korea must abandon its nuclear weapons program.
Despite that, Trump's statement that he would be "honoured" to meet Kim - as well as his description of the young North Korean leader over the weekend as "a pretty smart cookie" - sparked fresh concern over his approach to North Korea.
Tensions on the Korean peninsula have been high for weeks, driven by fears the North might conduct a long-range missile test, or its sixth nuclear test, around the time of the April 15 anniversary of its state founder's birth.
Pyongyang vowed to defy pressure
Early on Monday, North Korea said it would bolster its nuclear force "to the maximum" in a "consecutive and successive way at any moment" in the face of what it calls US aggression and hysteria.
North Korea, technically still at war with the South after their 1950-53 conflict ended in a truce, not a treaty, regularly threatens to destroy the United States, Japan and South Korea.
It said it will pursue its nuclear and missile programs to counter perceived US aggression.
Trump warned on Thursday that a "major, major conflict" with North Korea was possible, while China said last week the situation on the Korean peninsula could escalate or slip out of control.
In a show of force, the United States has sent the nuclear-powered USS Carl Vinson aircraft carrier group to waters off the Korean peninsula to join drills with South Korea to counter a series of threats of destruction from North Korea.