Chinese President Xi Jinping "is exerting a lot of influence from behind the scenes", said Bonnie Glaser, senior adviser for Asia at the Center for Strategic and International Studies in Washington.
The president has suggested strongly that the meeting with Kim ensured that North Korea was no longer a threat.
"There may be differences ahead between the DPRK (North Korea) and the U.S. in regards to denuclearisation, because the United States wants irreversible and verifiable denuclearisation".
Kim is expected to be received by Xi in Beijing. The presence of two vehicles marked for top-level North Korean officials has sparked speculation that Kim may be accompanied by his sister, Kim Yo-jong. Add North Korea as an interest to stay up to date on the latest North Korea news, video, and analysis from ABC News.
North Korean state media has not confirmed the trip, but Monday's Rodong Sinmun included an article noting that Kim had "sent a congratulatory letter and a floral basket to Xi Jinping ... on his birthday".
The two-day exercise - tiny compared with the suspended US-South Korea war games - will involve six warships and seven aircraft and had begun, Seoul's defence ministry said.
Donald Trump gives the North Korea leader Kim Jong-un a thumbs up at their historic meeting on Sentosa Island.
But that statement lacked specifications about how North Korea would dismantle its nuclear weapons program.More news: Watch fans cause mini natural disaster in Mexico City after game-winning goal
Kim "felt thanks for and highly praised China's promotion of denuclearisation of the Korean Peninsula and its important role in protecting the peninsula's peace and stability", state-run CCTV said.
US Secretary of State Mike Pompeo also visited Beijing last week during which China's Foreign Minister Wang Yi spoke of "the importance of China being a constructive participant in the next steps".
"We hope Chairman Kim Jong Un's visit will contribute to that".
But analysts say the Singapore summit has made it hard for the Trump administration to return to that policy even if its current diplomacy with North Korea proves to be a failure.
-North Korean denuclearization talks, having provided chartered aircraft for Kim to travel to and from Singapore for the summit. "I$3 hope both North Korea and the U.S. can carry out the outcomes of the leaders' summit and ... work together to push forward the peace process".
"There may be differences ahead between the DPRK and the United States in regards to denuclearization, because the USA wants irreversible and verifiable denuclearization. It may be hard for Kim Jong-un to accept", Hua said.
China has shown a willingness to be involved in U.S.
The U.S. government canceled military exercises with South Korea in the 1990s while attempting to negotiate with North Korea, but they were ultimately reinvigorated when Pyongyang balked at allowing inspectors to look at their nuclear sites.
This week's visit would likely see Beijing reward Kim for his recent diplomatic overtures, Xie continued.