"If it would be appropriate for me to meet with him, I would absolutely, I would be honored to do it," Trump said in a Bloomberg interview. "If it's under the, again, under the right circumstances. But I would do that."
Later Monday, White House spokesman Sean Spicer said that while the meeting could happen under the right circumstances, "those circumstances do not exist now." He added that there would have to be "significant change" for a meeting between Trump and Kim to be a possibility.
When a reporter pressed Spicer on why Trump would consider it an "honor" to meet with the North Korean leader, the press secretary said Kim is "still a head of state."
Spicer also said that Trump is "doing everything diplomatically, economically and militarily" to stave off the nuclear threat that North Korea poses to the United States.
The president's remarks come after North Korea conducted yet another failed missile test early Saturday, a move Trump said "disrespected the wishes of China."
As a candidate, Trump had expressed similar willingness to meet the North Korean leader. In a CBS interview that aired Sunday, Trump called the North Korean dictator "a pretty smart cookie," repeating other compliments of Kim that he made on the campaign trail.
When asked about these remarks, Spicer said Kim "assumed power at a young age" and has fended off potential threats to his rule.
"He's obviously managed to lead the country forward despite the obvious concerns that we and so many other people have. He is a young person to be leading a country with nuclear weapons," Spicer said, adding that the president does recognize the threat North Korea presents.
Kim's uncle, Jang Song Thaek, was executed in 2013 after being declared a traitor. He had long been considered the isolated nation's second in command and mentor to Kim. But North Korea's state news agency turned on Jang, claiming that he sought to capitalize on the death of Kim Jong Il and challenge his son, Kim Jong Un, to claim power for himself.
Trump's positive comments of Kim stand in contrast to those made by other political leaders.
On Friday, Secretary of State Rex Tillerson urged the United Nations to take new sanctions against North Korea. A day earlier, Tillerson said North Korea's closest major ally, China, has pledged to impose unilateral sanctions should Pyongyang carry out another nuclear test.
House Majority Leader Rep. Kevin McCarthy said on Thursday that the chamber would hold a vote on sanctions this week, which he said would target North Korea's shipping industry and "those who employ North Korean slave labor abroad."