In a wide-ranging news conference after congressional elections, Trump said he was willing to accede to North Korea's key demand of easing sanctions "but they have to be responsive to us."
Secretary of State Mike Pompeo had been set to meet Thursday in New York with a top North Korean official to arrange a new summit between Kim and Trump, who held a landmark meeting in June in Singapore.
But Pompeo abruptly postponed the talks in New York. Trump, asked about the delay, attributed it to a scheduling issue.
"We will make it another day. But we are very happy how it is going with North Korea," Trump said.
"But I will say this, I will say this very simply -- We are in no rush, the sanctions are on," he said.
North Korea has demanded that the United States end its tough sanctions now that it is negotiating with Trump on a deal to end its nuclear program.
But the Trump administration says that sanctions must remain as pressure until a final accord, rejecting an incremental approach favored by ally South Korea.
Trump repeated that he considered his outreach to Kim to be a major success, pointing out that North Korea has not tested further missiles since the diplomacy opened.
"We made more progress in that four or five months (since the summit) than they have made in 70 years," he said, referring to previous US leaders.
"And nobody else could have done what I have done," he said.