"If it would be appropriate for me to meet with him, I would absolutely, I would be honored to do it," Trump told Bloomberg News
in an interview Monday. "If it's under the, again, under the right circumstances. But I would do that."
No sitting US president has ever met with the leader of North Korea while in power, and the idea is extremely controversial.
White House press secretary Sean Spicer, however, said later on Monday that the US would first need to see changes in North Korean behavior before a potential sit-down.
"We've got to see their provocative behavior ratcheted down immediately," Spicer said. "Clearly, the conditions are not there right now."
Spicer also offered an explanation for Trump's view, expressed to CBS, that Kim is a "smart cookie."
"He assumed power at a young age when his father passed," Spicer said. "There was a lot of potential threats that could have come his way. He's managed to lead a country forward, despite the concerns that we and so many people have. He is a young person to be leading a country with nuclear weapons."
Speaking Tuesday, a Chinese official said "the only feasible way to a denuclearized Korean peninsula as well as peace and stability there is through dialogue and construction."
"This is also the only correct choice," Foreign Ministry spokesman Geng Shuang said, calling on all sides to "find a breakthrough in the resumption of peace talks as soon as possible."
Trump's comment about meeting Kim comes as tensions have risen in recent months between the US and North Korea as Pyongyang has sought to advance its nuclear and ballistic missile programs 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.
CIA Director Mike Pompeo arrived in Seoul over the weekend plans to attend internal meetings with US Forces Korea and embassy staff, according to Daniel Turnbull, a spokesperson for the US Embassy.
Despite pivotal elections in South Korea next week, Pompeo has no plans to meet with any of the presidential candidates. Leading candidates have promised a new era of relations with Pyongyang.
Trump said during the presidential campaign that he would be willing to meet with Kim Jong Un, explaining in June that "there's a 10% or 20% chance that I can talk him out of those damn nukes 'cause who the hell wants him to have nukes."
"I'll speak to anybody," Trump said then.
His comments received criticism from both sides of the aisle at the time, and since Trump has become president, top officials in his administration have taken a more equivocal position on the issue.
In the Bloomberg interview, Trump gave a nod to his willingness to take an unconventional approach.
"Most political people would never say that," he noted. "But I'm telling you under the right circumstances I would meet with him."
The North Korean nuclear issue has quickly become one of the top national security concerns for the Trump administration and administration officials have repeatedly stressed the increasing urgency of the situation. 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.
Mixed messages from the Trump administration regarding its policy on North Korea have also further obscured what the next phase of the standoff on the Korean Peninsula could be.
On Monday, White House chief of staff Reince Priebus told "CBS This Morning" that he could not see a scenario in which Trump and Kim sat down face-to-face unless Pyongyang was willing to "disarm and give up what he's put in mountainsides across his country and give up his drive for nuclear capability and ICBMs."
Speaking to NPR last week, Secretary of State Rex Tillerson indicated the US is willing to engage in talks with Pyongyang, a possibility dismissed in April by Vice President Mike Pence until North Korea denuclearizes.