SEOUL—North Korean leader Kim Jong Un gave the U.S. until the year’s end to break a deadlock in stalled nuclear talks, Pyongyang state media reported on Saturday, saying he remained open to a third summit with President Trump.

Mr. Kim, in his most direct remarks to Washington since February’s no-deal summit in Vietnam, said he doesn’t “need to persist” on pursuing another summit and isn’t desperate for sanctions relief, state media reported. He made the remarks on Friday at a gathering of North Korea’s rubber-stamp legislature, the Supreme People’s Assembly.

Mr. Kim warned the U.S. to change its approach to nuclear talks. He gave Washington “until late this year,” but added in an apparent reference to the Hanoi summit: “There won’t be as good an opportunity as last time.” The two leaders began discussions about North Korea’s nuclear disarmament at a summit in Singapore in June.

The North Korean leader called his personal relationship with Mr. Trump “great” and “not hostile,” state media reported.

Mr. Trump in a tweet Saturday wrote: “I agree with Kim Jong Un of North Korea that our personal relationship remains very good, perhaps the term excellent would be even more accurate, and that a third Summit would be good in that we fully understand where we each stand.” He made no mention of Mr. Kim’s year-end ultimatum.