On Wednesday, the North's military chief, Pak Jong Chon, also warned that the use of force against the North would cause a "horrible" consequence for the U.S. He said North Korea would take unspecified "prompt corresponding actions at any level" if the U.S. takes any military action.
During a visit to London on Tuesday, President Trump said his relationship with Kim was "really good" but also called for him to follow up on a commitment to denuclearize. "We have the most powerful military we ever had, and we are by far the most powerful country in the world and hopefully we don't have to use it. But if we do, we will use it," Mr. Trump said.
He added that Kim, "likes sending rockets up, doesn't he? That's why I call him rocket man."
CBS News "Face the Nation" moderator Margaret Brennan says the Trump administration will be preparing for a potential diplomatic crisis over the next three weeks ahead of North Korea's end-of-year deadline for a breakthrough in diplomacy. The U.S. is taking seriously the threat that North Korea could break its 18-month pause on nuclear or long-range weapons tests.
Administration officials would not say whether President Trump's revival of the "rocket man" moniker was a deliberate signal to the North of waning patience in Washington, but as Brennan notes, it appears to have gotten Pyongyang's attention, given the statements by North Korea in recent days.
In 2017, Mr. Trump and Kim traded threats of destruction as North Korea carried out a slew of high-profile weapons tests aimed at acquiring an ability to launch nuclear strikes on the U.S. mainland. The U.S. president said he would rain "fire and fury" on North Korea and derided Kim as "little rocket man," while Kim questioned Mr. Trump's sanity and said he would "tame the mentally deranged U.S. dotard with fire."
The two leaders have avoided such words and developed better relations after North Korea entered nuclear negotiations with the U.S. last year. Mr. Trump even said he and Kim "fell in love."
It was during a visit to London for a NATO summit this week that Mr. Trump used the phrase "rocket man" again, as he appeared to take the "Christmas gift" threat in stride. After he used the term, he added that he believed he still had "a very good relationship" with Kim.
The two men have met three times, starting with a summit in Singapore in June 2018. But their nuclear diplomacy has remained largely deadlocked since their second meeting in Vietnam in February ended without any deal due to disputes over U.S.-led sanctions on North Korea.
Trump's national security adviser Robert O'Brien said Thursday night in Washington the U.S. remains hopeful that a deal can be reached with North Korea.
"Kim Jong Un has promised to denuclearize the Korean Peninsula. We hope that he sticks to that promise, and we're going to keep at the negotiations and keep at the diplomacy as long as we think that there's hope there. And we do," O'Brien said Thursday night on Fox News Channel's "Special Report with Bret Baier."
"I don't want to say we're optimistic, but we have some hope that the Koreans will come to the table ... and we can get a deal."
North Korea threatened the U.S. earlier this week with a "Christmas gift" unless the Trump administration agrees to significantly ease sanctions as part of any resumed nuclear talks. As CBS News correspondent Elizabeth Palmer reported, those talks have been stalled since February.