It was the second meeting of the two leaders after their first on April 27.
"We'll see what happens".
"It could even be the 12th", he added.
President Moon Jae-in had earlier said he was "very perplexed" and that it was "very regrettable" that the summit was not going ahead. "We'd like to do it".
Moon and Kim were joined by South Korean intelligence chief Suh Hoon, who served as presidential envoy to North Korea, and Kim Yong Chol, senior North Korean official in charge of relations with South Korea, video clips show.
Utah man jailed in a Venezuela for two years to be released
Joshua Holt, 26, from Utah has been held in a Venezuelan prison on allegations of spying for the USA , according to reports. Orrin Hatch , R-Utah, who said Holt soon would be reunited with "his sweet, long-suffering family" in Riverton, Utah .
United States officials have talked about a comprehensive one-shot deal in which North Korea fully eliminates its nukes first and receives rewards later. "We are carefully watching the developments".
This picture taken on May 26, 2018 and released by the Blue House via Dong-A Ilbo shows South Korea's President Moon Jae-in (second L) and North Korea's leader Kim Jong Un (R) during their second summit at the north side of the truce village of Panmunjom in the Demilitarized Zone (DMZ).
Trump's conciliatory turn followed a statement by Kim's government saying it regretted Trump's action and remained willing to talk.
"We're going to see what happens", he was quoted as saying by the U.S. media.
"We consider it fortunate that the embers of dialogue between the USA and North Korea have not died and are now being revived", he said.
Mr Trump took to Twitter on Saturday to angrily dismiss media speculation that the summit, even if reinstated, could not now be held in Singapore in the existing time frame. It's a gulf which does not appear to have narrowed despite two, rare trips to Pyongyang by Secretary of State Mike Pompeo to meet with Kim.
Washington has made it clear it wants to see the "complete, verifiable and irreversible denuclearisation" of the North.
The Star Wars Boba Fett Movie Is Happening - James Mangold to Direct
Writer-producer Simon Kinberg , who worked on the X-Men movies and The Martian , is rumored to be partnering with Mangold. Jeter and a six-part young-adult series that took place between Episodes II and III of the prequel trilogy ".
Pyongyang has vowed it will never give up its nuclear deterrent until it feels safe from what it terms USA aggression.
It's been a tempestuous few days that have left close US ally and summit-matchmaker South Korea "perplexed"; North Korea's traditional ally China indignant that Trump was blaming it for changing Kim's hardening attitude; and officials in Trump's own administration struggling to stay up to speed with developments.
It also was unhappy about the North's failure to allow worldwide observers to verify the dismantling of the Punggye-ri test site, the staging ground for all six of its nuclear tests. The North Korean regime has said Kim is ready to talk to Trump "at any time".
Bolton had suggested in April that the US could follow the "Libya model of 2003, 2004", in which Libyan leader Muammar Gaddafi abandoned his nuclear program in exchange for sanctions relief before being killed in 2011 during a USA -backed uprising.
Trump, speaking Friday to graduates at the U.S. Naval Academy, did not mention North Korea directly, but he stressed the United States' military might. "We'd like to do it", he said.
May 25, North Korea expressed regret about the cancellation of the summit of heads of state and explained the solution to the American leader "a lack of will or lack of self-confidence".
But others said Trump's demonstrated willingness to walk away could yet extract further concessions from Pyongyang.
Fiat Chrysler Recalls 4.8 Million Cars Over Cruise-Control Flaw
In 2015, Fiat Chrysler booked a 602 million-euro ($705 million) after-tax charge, mainly for estimated future recall costs. The company is urging customers to follow the recall instructions and get the repairs done as soon as possible.