Taking to Twitter, he wrote: “North Korea has not conducted a Missile Test since November 28, 2017 and has promised not to do so through our meetings. I believe they will honor that commitment!”
Mr Trump’s comments came after he took many by surprise by accepting an invitation to meet with Mr Kim later this year. It remains unclear whether the meeting will take place and a location it yet to be decided.
North Korea has indicated they plan to refrain from testing missiles and nuclear weapons during talks with the US, according to South Korea’s National Security Advisor Chung Eui-Yong, who was speaking after officials from the South met with the North.
During his first year in office, Mr Trump has repeatedly criticised North Korea, which has launched as series of intercontinental ballistic missiles and conducted its sixth and largest nuclear test.
The leaders have regularly exchanged insults, with Mr Trump referring to the North Korean leader as “Little Rocket Man” and threatening the country with “fire and fury like the world has never seen.”
Mr Kim responded by calling Mr Trump a “dotard”.
Since the talks were announced, Mr Trump has maintained a positive tone about a potential resolution to the hostilities between the two nations.
Speaking at a rally in Pennsylvania, he urged the crowd not to boo when Kim Jong Un’s name was mentioned.
When the jeers began, Mr Trump said: “No, it’s very positive … no, after the meeting you may do that, but now we have to be very nice because let’s see what happens, let’s see what happens.”
Many were less convinced that the meeting would go to plan, with some responding to Mr Trump’s positive tweet on social media, with comments including “you are naïve!’’ and “you’re being played”.
No US President has ever met with a leader of North Korea while in office.
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The two countries do not have diplomatic relations and officials suggested it could take longer to arrange such a meeting than the intended month of May.
A national security official under former President Barack Obama, Samantha Vinograd, said: “There is no way that President Trump can be ready, by May, to have a high stakes negotiation on denuclearisation on the Korean Peninsula, it’s just impossible”.
Mr Trump also posted another message on Twitter, knocking the media’s response to the meeting plans.
He wrote: “In the first hours after hearing that North Korea’s leader wanted to meet with me to talk denuclearization and that missile launches will end, the press was startled & amazed. They couldn’t’t believe it.
“But by the following morning the news became FAKE. They said so what, who cares!”
He has also said that sanctions against North Korea would remain in place, despite the plans to meet.
Agencies contributed to this report.