"If it doesn't happen, maybe it will happen later. Maybe it will happen at a different time," Trump said in the Oval Office as he sat alongside South Korea President Moon Jae-in. "The meeting is scheduled as you know on June 12th in Singapore. And whether or not it happens, you will be knowing pretty soon."
"But it may not work out for June 12," Trump later added. "But there is a good chance that we will have the meeting."
Separately, Secretary of State Mike Pompeo – the highest-ranking U.S. official to have met Kim – said he was not a betting man, but had greater confidence the meeting would take place.
"We're still working toward June 12th," he said later Tuesday, adding, "I'm optimistic, but again, this could be something that comes right to the end and it doesn't happen."
Responding to reporters' questions in his meeting with Moon, President Trump also appeared to imply again that Chinese President Xi Jinping may have personally pressured Kim to take a stronger stance in negotiations ahead of the summit.
"I will say I'm a little disappointed because when Kim Jong Un had the meeting with President Xi in China, the second meeting," Trump said. "I think there was a little change in attitude from Kim Jong Un. So I don't like that. I don't like that. I don't like it from the standpoint of China."
"Now maybe nothing happened," Trump added. "I'm not blaming anybody. But maybe nothing happened and maybe it did. There was a different attitude by the North Korean folks after that meeting."
Pompeo also had a different line on that, praising China's "historic assistance" with the international sanctions on North Korea. "We have every reason to expect that they will continue to do so," he added.
He said he believed Kim was "very serious" about his previously expressed desire to denuclearize the Korean peninsula.
"I do think he is serious," Trump said. "I think that he would like to see that happen."
But the president again tempered expectations about what the final outcome of any negotiations could be, saying there is "a very substantial" chance that an agreement "won't work out."
"You never know about deals. You go into deals that are 100% certain, it doesn't happen," Trump said. "You go into deals that have no chance and it happens. Sometimes happens easily. I've made a lot of deals."
President Trump also declined again to say whether he has directly spoken yet with Kim when asked by ABC News.
"I don't want to say that. I don't want to," Trump said. "There is no reason to discuss that."
But he again went out of his way to reassure Kim.
"I will guarantee his safety. Yes. I will guarantee his safety. And we talked about that from the beginning. He will be safe. He will be happy. His country will be rich."
The two leaders are meeting a week after North Korean leaders indicated the June 12 Singapore sit-down between Trump and Kim could be on shaky ground.
According to South Korea's Yonhap news, President Moon's national security adviser, Chung Eui-yong told reporters during the flight to Washington "there is a 99.9% chance the North Korea-U.S. Summit will be held as scheduled," but added, "we're just preparing for many different possibilities."