At a campaign rally for Republican congressional candidate Rick Saccone in western Pennsylvania,Trump said he believed North Korea wanted to make peace.
But he added he might leave the talks quickly if it didn't look like progress for nuclear disarmament could be made.
"Hey, who knows what's going to happen?" said Trump. "I may leave fast or we may sit down and make the greatest deal for the world."
A time and place to meet has not yet been set, although the meeting is supposed to happen by the end of May.
The North Korean leader’s invitation was relayed by a South Korean delegation who visited the White House.
No sitting US president has ever met a North Korean leader and Trump's decision to accept an invitation from the North Korean leader reportedly took top administration officials by surprise.
The move abruptly reversed decades of Washington policy aimed at preventing Pyongyang from developing nuclear weapons and ballistic missiles.
The United States has long said it wants any talks to aim at North Korea abandoning its nuclear weapons and missile programs.
Hopes for a breakthrough had risen on Thursday when Trump said he was ready to meet with Kim, who had invited Trump to what would be unprecedented talks between leaders of the two nations.
