He said the North must meet conditions for the summit to go ahead though if it did not, it might happen "later".
He was speaking as he received South Korea's President Moon Jae-in at the White House.
The North has said it may cancel the summit if the US insists on it giving up nuclear weapons unilaterally.
Mr Trump did not say what conditions the US had set for the summit but, asked by a reporter about the North's arsenal, he said "denuclearisation must take place".
The 12 June summit is due to take place in Singapore. It follows a summit between the two Korean leaders in April.
North Korea is expected to dismantle a nuclear test site this week as a good will gesture but the demolition may be delayed by bad weather.
"We'll see what happens," he told reporters.
"There are certain conditions that we want and I think we'll get those conditions and if we don't we don't have the meeting."
The property tycoon-turned-politician added: "You never know about deals. You go into deals that are 100% certain - it doesn't happen. You go into deals that have no chance and it happens and, sometimes, happens easily."
He also said Kim Jong-un's attitude had changed after his second visit to China, earlier this month.
Later in the day, during a news conference, Secretary of State Mike Pompeo adopted a more positive position, saying the US was still working towards the 12 June date for the summit.
He commended China for offering "historic assistance" in putting pressure on North Korea.