Trump's taunt of Kim came after the North Korean leader again called him a “dotard,” a term describing an old person who is losing his mental faculties. Trump, 71, sarcastically responded that he hopes one day to be friends with Kim, who oversees a developing nuclear weapons and ballistic missile arsenal.

Later, after a bilateral meeting with Vietnamese President Tran Dai Quang, Trump was asked at a joint news conference whether he thought it really was possible to be friends with Kim.

“I believe it's possible. Strange things happen in life,” Trump said. “If it did happen, it would be a good thing for North Korea, and a good thing for lots of other places and good for the world. Certainly it's something that could happen. I don't know if it will, but it would be very, very nice if it did.”

Watch more!

White House chief of staff John Kelly, chatting briefly with reporters after Trump's press conference Sunday in Hanoi, was asked about the president's descriptive tweet about the North Korean leader. Kelly dismissed the question, saying he and his West Wing team try not to react to their boss's tweets.

“We don't, I don't, I don't allow the staff to,” Kelly said, adding that the tweets “are what they are.”

Kelly said the White House staff prepared Trump for the trip in more traditional ways: “We did the staff work, got him ready to go, and then at each place we brief him up on whatever the next event is and all that,” he said. “The tweets don’t run my life — good staff work runs it.”

On Twitter and at the news conference, Trump also returned to a favorite theme of bashing critics who have accused him of being soft on Russia in the wake of special counsel Robert S. Mueller III's ongoing investigation into his campaign's ties to Russian officials and possible attempts at collusion. Trump has denied that his campaign coordinated in any way with Moscow during last year's presidential campaign, and he said Saturday that Russian President Vladimir Putin again denied any involvement in trying to influence the U.S. elections when Trump spoke with him at a regional summit in Danang, Vietnam.

On Twitter, Trump also slammed President Barack Obama and former secretary of state Hillary Clinton for failing to improve relations with Russia.