Since the Kim-Trump summit in Singapore in June 2018, discussions between Pyongyang and Washington over the North's nuclear arsenal have stalled.
The US insists that sanctions must remain in place until it gives up its weapons, and the North is demanding an immediate easing.
In his New Year's address, Kim warned that if Washington persisted with its approach, "we may be compelled to find a new way for defending the sovereignty of the country and the supreme interests of the state".
Kim is taking a heavy delegation to Beijing. According to the state-run Korea Central News Agency, the leader went by special train, accompanied by his wife Ri Sol-ju, generals Kim Yong-chol and No Kwang-chol, vice Marshal Ri Yong-ho and top party leader Pak Thae-song.
With his visit to China, "Kim is eager to remind the Trump administration that he does have diplomatic and economic options besides what Washington and Seoul can offer," said Harry Kazianis of the Center for the National Interest in Washington quoted by AFP.
The US should be "quite concerned" by any effort by Pyongyang to strengthen ties with Beijing, he added, as almost all North Korean trade flows through China and any improvement in relations would weaken the Trump administration's "maximum pressure" strategy.
With US and Chinese officials meeting in Beijing to address a trade row that has roiled global markets, he says the timing could not be any better for the Chinese side. "It shows Beijing clearly has a North Korea card to play if it sees fit."
Meanwhile, China and the US are watching each other closely in the region.
Army publication Stars and Stripes reported that “The USS McCampbell guided-missile destroyer sailed within 12 nautical miles of the Chinese-claimed Paracel ("Xixia") Islands in a freedom-of-navigation mission Monday,” quoting 7th Fleet spokesman Cmdr. Clay Doss.
China reacted angrily and Foreign Ministry spokesman Lu Kang told reporters on Monday that China dispatched planes and ships to demand that the USS McCampbell leave waters around the Paracel Islands.
Lu said the destroyer was in the area Monday without China's permission and "we have made stern complaints with the US."