Trump tweeted, "North Korea fired off some small weapons, which disturbed some of my people, and others, but not me. I have confidence that Chairman Kim will keep his promise to me, & also smiled when he called Swampman Joe Biden a low IQ individual, & worse. Perhaps that's sending me a signal?"
A Biden campaign aide responded after the tweet, saying, "I would say the tweet speaks for itself, but it's so unhinged and erratic that I'm not sure anyone could even say that with a straight face."
The same aide said of the president's tweet correcting the spelling of Biden's name: "The spelling error was not the main problem with the first one."
While Trump has tried to spin North Korea's recent launch, both Bolton and Japan have accused North Korea of violating U.N. resolutions. Bolton's comments were the first time a U.S. official said North Korea was in violation.
The Trump administration is trying to keep diplomatic doors open to North Korea, even though Bolton admitted the U.S. has not "heard much" from North Korea since the summit in Hanoi fell apart. He said U.S. Special Envoy to North Korea Stephen Biegun has not received contact from his counterpart in Pyongyang.
Bolton also said he supports Japan's efforts to sit down for negotiations with Kim. Abe still has not met with the North Korean leader.
Japanese officials said that during Trump's four-day state visit, Abe will be introducing Trump to the families of Japanese abducted by North Koreans. Trump had a similar meeting during his last visit to Japan. The release of Japanese abductees is a top priority for Abe.
Despite the defense of Kim, the two foreign leaders appeared to be getting along great on the golf course Sunday. Abe tweeted a photo of the two smiling from the course talking about an "unwavering" alliance between the two countries in Japanese.
After the pair hit the links, Trump stated on Twitter the two world leaders have made "great progress" in the trade negotiations, but indicated he may wait until after July to announce any potential deal.
Trump himself tweeted about the round of golf -- a pastime both leaders have bonded over -- and his love for former South African great and nine-time major champion Gary Player.
After golf, Trump and Abe sat down for talks at Akasaka Palace, Japan's state guest house.
"We've had some great talk on trade, we've had a great talk on the military and we discussed, of course, North Korea, and I think we made a lot of progress on a lot of subjects," Trump said. "This is the best relationship that we've ever had with Japan."
Trump and Abe also discussed the situation in Iran.
"Nobody wants to see terrible things happen," Trump added. "Especially me."
ABC News' Rachel Scott contributed to this report.