However, the United States president said later that conversations were underway with North Korea and a canceled summit with Kim Jong-un could go ahead on "the 12th", an apparent reference to June 12, the previously scheduled date of the meeting.
After Trump's latest missives about the possibility of the summit being held as scheduled, a spokesman for South Korea's presidential Blue House called the move a "fortunate" development.
White House spokeswoman Sarah Sanders said a team of White House and US State Department officials would leave for Singapore on schedule this weekend for the planned 12 June summit.
Trump scrapped the meeting, planned for Singapore, in a letter to Kim on Thursday after repeated threats by North Korea to pull out over what it saw as confrontational remarks by USA officials demanding unilateral disarmament.
In a tweet Friday, the president said his administration is having very productive talks with North Korea about reinstating the meeting.
Trump had earlier indicated the summit could be salvaged after welcoming a conciliatory statement from North Korea saying it remained open to talks.
"They exchanged views and discussed ways to implement the Panmunjom Declaration and to ensure a successful US North Korea summit", the Blue House said in a statement, adding Moon would make a personal statement on Sunday morning. "We'd like to do it".
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Trump told reporters at the White House that both sides would like the summit to happen.
In separate speeches last month, Kim and Moon promised a new era.
On Friday, North Korea issued a statement saying it was still "willing to give the USA time and opportunities" to reconsider talks "at any time, at any format".
He said, "The best way to prevent war is to be fully prepared for war". There, former leader Colonel Gaddafi gave up his nascent nuclear programme only for him to be killed by Western-backed rebels a few years later. Kim wants to make a "grandiose proposal", he said, such as denuclearization in exchange for normalizing relations, but agreeing to that without working out the finer points could have serious ripple effects, including taking away the legal justification for US troops on the peninsula.
In canceling the meeting, Trump cited hostile comments from top North Korean officials as well as concern about the country's commitment to giving up its nuclear weapons.
"Today's summit is aimed at resolving the misunderstanding caused by communication glitches between Washington and Pyongyang and lay the groundwork for the US-North Korea summit", he told AFP. Then on Friday, he said "everybody plays games" and hinted that the summit might happen after all.
But with the summit in doubt, Wit said, North Korea is moving to Plan B, which is to ensure the goodwill it established with South Korea, China and Russian Federation in recent months is not squandered.
South Korea's government said in a statement released Saturday that it was relieved about the revived talks for a summit. They met with Choe Son Hui, the North Korean vice foreign minister, the Post said.