The demolition of the 60-foot-tall cooling tower at its main reactor complex in Yongbyon North Korea on June 27, 2008.
He added: "That doesn't mean that it won't work out over a period of time, but it may not work out for June 12".
It was the clearest indication to date that the audacious summit Trump agreed to in March may be at risk.
Mairead Maguire, the 1976 Nobel Peace Prize laureate, and dozens of other female activists from around the world will march toward the Demilitarized Zone (DMZ) this week in a campaign to call for lasting peace with North Korea.
"I have no doubt that you will be able to. accomplish a historic feat that no one had been able to achieve in the decades past", Moon said.
The former Central Intelligence Agency director, who has met twice with Kim since the start of April, told the committee that it's his hope that when Trump and Kim confer, "we can get the North Koreans to make this strategic shift about how best to serve the country - that the nuclear weapons program isn't in fact the thing that keeps the regime in power, but the thing that prevents the regime from being in a place it wants to be with economic success".
Mr Trump said: "If it doesn't happen, maybe it happens later", reflecting recent setbacks in efforts to bring about reconciliation between the two Koreas. "But we are talking".
His statement followed Trump's suggestion on Tuesday that the meeting could be delayed or scrapped entirely.
Tests staged at the site have demonstrated the country's rapid progress in its nuclear programme - especially since Kim took power in 2011 and oversaw four atomic tests in only six years.
That, in turn, has led to skepticism the summit between Trump and Kim will proceed.
Mr Trump said he had noticed "a little change" in Kim Jong-un's "attitude" after Kim took a second trip to China this month in the run-up to the summit.
The country's first test was largely seen as a failure and produced an estimated yield of only about one kiloton, compared to as much as 250 kilotons in the sixth - an explosion 16 times more powerful than the USA atomic bomb dropped on Hiroshima in 1945.
And he suggested Pyongyang had much to gain from striking a deal. "I think they should seize the opportunity, and we'll soon find out whether or not they want to do that", Trump said while addressing reporters at the White House on May 22. And I think things changed after that meeting.
Last week Kim, upset over US-South Korea military drills and indelicate comments by US national security adviser John Bolton, threatened to pull out of the June 12 summit, and Trump admitted yesterday the meeting was in doubt.
There was no word on how the South Korean reporters might reach North Korea to catch up with their colleagues.
"We are prepared", he said.
Moon arrived at the White House at noon EDT (7pm Kenyan time) for a meeting and a working lunch and left less than two hours later.
He did meet with some of Trump's aides earlier in the day, however, as questions about the administration's approach to the summit continue to mount.
"It can't be a great country under the circumstances they're living in right now. But we're talking right now".
Pompeo, who was director of the Central Intelligence Agency under Trump before becoming secretary of state in April when the president fired Rex Tillerson, has met twice with Kim in Pyongyang.
Go Myong-hyun, an analyst at the Asan Institute for Policy Studies, said both sides were playing "a game of chicken" in the run up to the summit "to gain an upper hand in negotiations". "We remain open to it, we remain hopeful", Vice President Mike Pence said on Fox Radio Tuesday.
Regardless of the site's current state, the North Koreans seem keen to control even what the journalists invited to view its destruction can learn about it. "There have been no concessions offered and none given".