Trump made the reference to the North Korean leader in a tweet Sunday.
I spoke with President Moon of South Korea last night. Asked him how Rocket Man is doing. Long gas lines forming in North Korea. Too bad!
"The interesting thing about the Trump policy is the Trump policy I think has been right in what they've been trying to do," said Burns, who was undersecretary of State for political affairs during the George W. Bush administration.
"The president's public remarks have been off. 'Rocket Man' [is] probably not the best things to say even to a brutal leader like Kim Jong Un," Burns added in an interview on CNBC's "Squawk Box."
Trump will address the United Nations General Assembly in New York on Tuesday and is expected to touch on the crisis that has seen the president and Pyongyang trade threats of military action. North Korean diplomats will also be present.
Burns, who also was U.S. ambassador to NATO, said there likely will be no deals behind the scenes between Trump and other leaders at the U.N. meeting. "This is going to be a slow-moving crisis. There's no short-term fix," he said.
Trump's mission will be attempting to persuade other world leaders to put on tough economic sanctions against North Korea, Burns said.
Burns said Kim wants to achieve strategic "equilibrium" with the U.S. and the rest of the world.
"I think he's close to achieving that, unfortunately," Burns said. United Nations sanctions are not enough for him to give up his nuclear weapons, Burns added.