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President Donald Trump mocked North Korean dictator Kim Jong Un in a tweet on Saturday, after that country's foreign ministry called the U.S. president “an old lunatic.”

"Why would Kim Jong-un insult me by calling me "old," when I would NEVER call him "short and fat?" Trump tweeted Saturday night ET while on an 11-day Asia trip, during which North Korea has been a frequent topic.

"Oh well, I try so hard to be his friend - and maybe someday that will happen!" Trump tweeted. Trump is 71. Kim's official age is unclear but he is thought to be 33, according to a date of birth used by the U.S. Treasury Department.

But in a day of presidential contradiction, Trump seemed to take a softer tone in the Vietnamese capital of Hanoi around three hours after his tweet.

Trump said a friendship with Kim Jong Un "could happen," allowing that "Strange things happen in life. That might be a strange thing to happen, but it's certainly a possibility."

"If that did happen it would be a good thing for, I can tell you, for North Korea — but it would also be good for lots of other places and it would be good for the world," Trump said.

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"I don't know that it will" happen, Trump said, "but it would be very, very nice if it did."

Conway on Trump's tweet on Kim Jong Un: That "was the president just responding the way he does to somebody who insulted him first." pic.twitter.com/8xsEMStIYL — This Week (@ThisWeekABC) November 12, 2017

Trump and North Korea, and once Kim himself, have engaged in a war of words in recent months over North Korea's nuclear and missile programs, international sanctions levied against North Korea and other issues.

Trump referred to Kim as "rocket man" during his first speech before the United Nations in September. Kim, in a personal dispatch written in the first person, responded by calling Trump a "dotard."

"All responsible nations must act now to ensure that North Korea’s rogue regime stops threatening the world with unthinkable loss of life," Trump said Sunday morning.

"We want progress, not provocation — I mean we, we have been provoked, the world has been provoked, — we don't want that," Trump said. "We want stability, not chaos, and we want peace, not war."

Related: What to Know About North Korea's Dictator Kim Jong Un

North Korea has conducted six nuclear tests — its most recent test was in early September — and this year twice conducted intercontinental ballistic missile tests. Experts have said those tests suggest a missile could reach parts of the United States.

North Korea's foreign ministry in an official statement Saturday said "Reckless remarks by an old lunatic like Trump will never scare us or stop our advance," according to The Associated Press. An NBC translation of the statement has the ministry referring to Trump as a "dotard." A dotard is an arcane term for a senile or weak-minded elderly person.

Related: North Korea Says Trump 'Begged' for Nuclear War During Asia Trip

Trump warned North Korea not to underestimate the United States during a speech to South Korea’s National Assembly on Wednesday.

"The regime has interpreted America's past restraint as weakness," Trump said as he wrapped up the South Korean leg of his Asia tour. "This would be a fatal miscalculation. This is a very different administration than the United States has had in the past."

"I say to the North: Do not underestimate us, and do not try us," Trump said in Seoul.