SINGAPORE — President Trump exuded confidence Monday on the eve of his landmark meeting with Kim Jong-un of North Korea. But American and North Korean diplomats were engaged in difficult last-minute negotiations to bridge gaps on some of the most basic issues dividing the two sides.

Mr. Trump, who spent much of the day talking to other Asian leaders about the high stakes of his encounter with Mr. Kim, told Singapore’s prime minister, Lee Hsien Loong, that he was bullish about the outcome.

“I just think it’s going to work out very nicely,” he said.

While Mr. Trump had lunch with Mr. Lee under a glittering chandelier in the prime minister’s ceremonial offices, a team of American diplomats was meeting at a nearby hotel to try to lock down the language of a joint communiqué to be issued by Mr. Trump and Mr. Kim at the end of their meeting.

The statement is likely to have three sections — dealing with denuclearization, security guarantees for the North and steps to be taken by both sides — according to a person briefed on the talks. But it was not clear that the Americans would succeed in extracting a more detailed commitment to disarming than North Korea has already offered.