Speaking to reporters at the White House, the president stressed he would still insist on the isolated regime dismantling its nuclear program. Asked if Kim is bluffing by suggesting he could pull out of the summit, Trump responded, "we'll see what happens."
"We haven't been notified at all," the president said.
In an earlier statement delivered by a state news agency, North Korean First Vice Minister of Foreign Affairs Kim Kye Gwan said Pyongyang would reconsider the meeting if the U.S. insists on denuclearization. The summit is set for June 12 in Singapore.
The State Department has said it will plan as if the summit will still happen.
Earlier in the week, North Korea canceled a planned meeting with South Korea. The regime called joint U.S.-South Korea military drills a "provocation" and preparation for an invasion, according to reports.
The developments threaten a historic meeting during which the U.S. hoped to make strides toward Pyongyang abandoning its nuclear and missile programs. The U.S. and its allies such as South Korea and Japan have used economic sanctions to try to deter North Korea's development of nuclear weapons.
Trump has repeatedly insisted on full denuclearization of the Korean Peninsula. The U.S. has also suggested it may not be willing to reduce its military presence in South Korea, something North Korea could insist on as part of nuclear talks.
The top Senate Democrat, Chuck Schumer of New York, urged Trump on Wednesday not to give Kim "anything for free." In a tweeted statement, the Senate minority leader said, "We must be strong, and we must be resolute — this exercise should move forward."