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.
"We'll see what happens". He said: "They very much want to do it, we'd like to do it".
"We will soon see where it will lead, hopefully to long and enduring prosperity and peace", he tweeted.
South Korea's government said in a statement released Saturday that it was relieved about the revived talks for a summit. They punched posters with Trump's picture and called the move a betrayal. His decision on Thursday to call off the summit appears to not have stuck.
After the summit between him and South Korean President Moon Jae-in last month, a poll by the Korean Research Center found 78 per cent of South Koreans said Kim is "trustworthy", a big change in attitudes given his previous infamy here. Defense Secretary Jim Mattis told reporters diplomats were "still at work" and said Trump had just sent a note out on the summit, which could be back on "if our diplomats can pull it off".
Other South Koreans say it's not their optimism that's misplaced, but their trust in Trump. Even as his aides express doubt the summit can be arranged in the next 18 days, Trump has told confidants and advisers he believes the original date may still hold. "We didn't want to go to a meeting just for the sake of going to a meeting. There had to be something to come out of it".
"Sadly, based on the tremendous anger and open hostility displayed in your most recent statement, I feel it is inappropriate, at this time, to have this long-planned meeting", read Trump's letter to Kim.
USA officials argue that the administration has already won a great deal from North Korea, including a moratorium on missile testing and the release of three American prisoners, without giving up anything in return.
Trump too has warned that Kim could face a bloody end if he does not give up his nuclear weapons program, but he has also publicly committed to Kim's safety and security if he does. In the first year of Donald Trump's presidency, Pyongyang made this reality abundantly clear by carrying out its sixth (and most powerful) nuclear test and a number of ballistic-missile launches.
North Korea later said it was willing to talk "at any time in any form".
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These proposed changes, the archbishop concluded, have united all Christian traditions [around the "No" campaign]. Ireland does not give its expatriates absentee ballots or the option to vote at embassies.
"They committed to remaining closely coordinated in all of their efforts to create conditions for dialogue with North Korea and agreed that must continue until North Korea embraces denuclearization", Nauert said in a statement.
It was unclear whether Trump was engaged in what he saw as a negotiating ploy or if his moves were a manifestation of mounting internal concerns over ensuring a successful outcome for the summit.
China's Vice President Wang Qishan found encouragement in the continuing exchanges between the US and North Korea. "They simply stood us up", one White House official said, according to the Washington Post.
"This meeting may still happen, and it may not", she said.
Trump's announcement was met by a melange of puzzlement, outrage and profound anxiety across the world. And, maybe, North Korean leader Kim Jong-un is someone you can trust.
"If there is a summit ..."
"The North Koreans didn't tell us anything, they simply stood us up", the official said.
"Everyone has to lower their expectations for a summit".
However, the North quickly became angered by comments from senior USA officials who made comparisons with Libya.