Trump and Kim are set to meet in Singapore on Tuesday morning, with the U.S. president fresh off the G-7 summit last weekend in Canada.
"That was a very distributing performance by the president," Burns said on "Closing Bell," referring to Trump's behavior at the meeting of the Group of Seven industrialized nations.
On Sunday, Trump refused to endorse a declaration calling for a reduction in tariffs and lashed out at U.S. allies for allegedly treating the United States unfairly.
"He increasingly is seen by other leaders around the world, our friends and allies as well as our opponents, as someone who's a little bit erratic and unstable and unpredictable and doesn't keep his word," said Burns, who served as U.S. ambassador to NATO and was the State Department's third-ranking official during George W. Bush's presidency. He also advised the administrations of George H.W. Bush and Bill Clinton.
He thinks leaders in both North Korea and China may be a bit more reluctant to sign up to a series of commitments with the U.S. given the "havoc" the president created at the G-7.
"You can bet the North Koreans are watching closely. It may make them back off. It may make the Chinese back off going down this road the way that the United States wants to do it on this nuclear issue," said Burns, also a CNBC contributor.