Trump, who has met Kim three times since 2018 over ending the North's missile and nuclear programs, addressed Kim directly, referring to the one-party state's ruler as "Mr. Chairman."
In his tweet, Trump told Kim, "You should act quickly, get the deal done," and hinted at a further meeting, signing off "See you soon!"
North Korea said on Thursday it had turned down a U.S. offer for fresh talks ahead of a year-end deadline Pyongyang has set for Washington to show more flexibility in negotiations.
U.S. Defense Secretary Mark Esper announced in Thailand earlier on Sunday that joint U.S.-South Korean military drills would be postponed in an effort to bolster the stalled peace push.
Pyongyang's official KCNA news agency in a commentary on Friday lashed out at Biden for insulting Kim, calling Biden a "rabid dog" that needs to be put down.
Biden tops most national opinion polls in the Democratic Party's nominating contest to take on Republican President Trump in a November 2020 election."Joe Biden may be Sleepy and Very Slow, but he is not a “rabid dog,” Trump tweeted. "He is actually somewhat better than that, but I am the only one who can get you where you have to be."