In his fullest response to Pyongyang’s threat to cancel, the US president undermined his own national security adviser by saying the “Libya model” was not being used.
Mr Trump also promised Kim “protections” if he agreed to meet in Singapore as originally planned – an olive branch to North Korean leader.
The comments were made in the White House on Thursday as Mr Trump was meeting Jens Stoltenberg, the Nato secretary general.
The US president was due to meet Kim in Singapore on June 12 to discuss denuclearisation but the North Koreans unexpectedly said this week they could pull out of the meeting.
US-South Korean military drills, comments made by John Bolton, Mr Trump’s national security adviser, and demands for the regime to “unilaterally” give up its nuclear programme were all cited as reasons.
But Mr Trump pointed the finger at another factor – Kim’s second meeting with with Xi Jinping, the Chinese president, earlier this month.
Mr Trump said there was a “big difference” in North Korea’s position since the meeting and suggested that Mr Xi “could be influencing” Kim.
China has traditionally been North Korea’s closest ally and reportedly feared being alienated from talks as Mr Trump pushed ahead with his plan for a face-to-face meeting.
Mr Trump also dismissed Mr Bolton’s own suggestion last month that the “Libya model” from 2003 and 2004 would be used by America for talks with North Korea.
Muammar Gaddafi, the Libyan leader, was convinced to give up his nuclear programme at the time. However he was later toppled and killed in 2011.
North Korea singled out Mr Bolton and his Libya plan in a lengthy criticism of America’s position as they threatened to pull the plug on the Trump-Kim summit.
Mr Trump said on Thursday that the Libya model had led to “total decimation” and would not be used for his talks – addressing one of Pyongyang’s concerns.
The US president also said he was “willing to do a lot” for a deal with North Korea and told Kim he would “get protections that would be very strong”.
Mr Trump predicted Kim would be “very, very happy” if he struck an agreement, adding: “I think the best thing he could do is to make a deal.”