The US President also said it would be a "good thing" for the world if he and Kim could become friends
Donald Trump has sarcastically declared he would never describe Kim Jong Un as "short and fat", in a series of tweets that also saw him take aim at the "haters and fools" critical of his push for closer ties with Russia.
The US President fired off half a dozen messages ahead of his official welcoming ceremony in the Vietnamese capital Hanoi, which he is visiting as part of his Asia tour.
Utilising Twitter's new 280-character tweet length Mr Trump gave his thoughts on a range of subjects - including relations with Russia, China's efforts to rein in North Korea, and a sarcastic message about his bid to make "a friend" of Kim.
The spectre of Pyongyang's nuclear weapons programme has loomed large over the President's trip, with one of the aims of tour to persuade China to put more pressure on the North.
A stern speech from Mr Trump in South Korea prompted Kim's government to brand him an "old lunatic" - the latest broadside in a long-running war of words between the two leaders.
Mr Trump took exception to being called "old":
Why would Kim Jong-un insult me by calling me "old," when I would NEVER call him "short and fat?" Oh well, I try so hard to be his friend - and maybe someday that will happen!— Donald J. Trump (@realDonaldTrump) November 12, 2017
Mr Trump later toned down his rhetoric when asked about the tweet during a joint press conference with Vietnam's president, Tran Dai Quang.
He said it would be a "good thing" for North Korea and the world if he and Kim could become friends, saying it "might be a strange thing to happen but it's certainly a possibility".
In another message, Mr Trump said there had been progress on getting China to up the pressure on its neighbour:
President Xi of China has stated that he is upping the sanctions against #NoKo. Said he wants them to denuclearize. Progress is being made.— Donald J. Trump (@realDonaldTrump) November 11, 2017
Also on the trip, Mr Trump met with Russian President Vladimir Putin several times on the margins of a summit in Vietnam.
He said he asked the Russian leader if he interfered in the 2016 US election and received assurances from Mr Putin that he "absolutely did not meddle".
The President said he had "good discussions" with his Russian counteraprt on Syria, writing:
Speaking to reporters on Air Force One while making his way to Hanoi on Saturday, Mr Trump said he believed the Russian leader was being sincere when he denied meddling.
"I really believe that when he tells me that, he means it," he said.
Mr Trump called the claim an "artificial barrier" put up by Democrats and once again cast doubt on the conclusion from his own intelligence agencies that Russia tried to interfere in the presidential poll to ensure Hillary Clinton was defeated.
"Having a good relationship with Russia's a great, great thing. And this artificial Democratic hit job gets in the way," Mr Trump said. "People will die because of it."