Foreign ministry spokesman Lu Kang said the sides should ensure the meeting runs as planned and yields “substantial outcomes”.
Mr Kim and Mr Trump are due to meet in Singapore on June 12, but Pyongyang has threatened to withdraw, saying it has no interest in a “one-sided” affair meant to pressure it into abandoning its nuclear weapons.
Mr Lu said the meeting was crucial to reducing tensions on the Korean Peninsula and maintaining regional peace and stability.
The North’s warning came hours after it abruptly cancelled a high-level meeting with South Korea, in protest over US-South Korean military exercises.
A senior Japanese official said Tokyo considers the US-South Korean joint exercise, along with those between the three allies, as key pillars of deterrence in the region.
Deputy chief cabinet secretary Yasutoshi Nishimura said Japan is moving ahead with the preparation for planned talks between the North’s leader Kim Jong Un and President Trump in the hopes they would provide a momentum toward comprehensively resolving North Korea’s problems.
Mr Nishimura said Japan will continue to cooperate with the US and South Korea and they agree on the need to maintain sanctions until the North changes its current policy.
He said: “We believe that steady implementation of the US-South Korea joint military exercise is important to maintain the regional peace and safety.”
South Korea’s defence ministry said the exercises will go on.
Spokeswoman Choi Hyunsoo said the Max Thunder drills are chiefly about improving the skills of pilots, and are not attack exercises.
The drills, which began on Monday and reportedly include some 100 aircraft, will continue until May 25.
The North has long denounced the military exercises between the rivals as invasion rehearsals.
Earlier, the US said it is going ahead with plans for the meeting between Mr Trump and Mr Kim.
US state department spokeswoman Heather Nauert said the US has not heard anything directly from Pyongyang or Seoul that would change that.
She said Mr Kim had previously indicated he understood the need and purpose of the US continuing its long-planned joint exercises with South Korea.