The motorcade likely carrying Mr Kim was later seen leaving Zhongnanhai, China's central leadership compound next to Beijing's Forbidden City.
"I think Chairman Kim Jong Un's visit to China will have a very positive effect on the success of the second US-North Korea summit", Moon told reporters.
Shi Yinhong, an worldwide relations professor at Renmin University in Beijing, said Kim's trip would have no direct influence on the progress of trade talks.
For his part, Kim said North Korea will make efforts to "achieve results that will be welcomed by the worldwide community" at the next summit with the United States, China's official news agency added.More news: Jurgen Klopp blames windy conditions for Liverpool's FA Cup defeat at Wolves
Relations between China and North Korea had deteriorated in recent years over Pyongyang's nuclear activities, but Mr Kim has made sure to keep Mr Xi informed about his dealings with the US and South Korea, and ties appear to have warmed.
"The Korean peninsula situation has been easing since a year ago, and China's important role in this process is obvious to all ... the DPRK side highly and sincerely appreciates the Chinese efforts", Kim said.
He said North Korea needed to take "bold steps" towards denuclearisation in order to draw USA concessions such as sanctions relief.
During his annual New Year's Day address last week, Kim said it was his "firm will" that North Korea will no longer produce or test nuclear weapons.
Kim's visit coincided with negotiations between USA and Chinese officials in Beijing to resolve a bruising trade dispute between the world's two largest economies that has roiled financial markets.More news: AMD Announces Radeon VII: 7nm Vega Coming to the Consumer Market
Kim emerged from his quarters around 4 p.m.to meet with Chinese President Xi Jinping at the Great Hall of the People, where Kim's wife Ri Sol-ju joined them later. Critics worry a peace declaration could undermine the justification for the USA military presence in South Korea. He left there around noon, Yonhap reported. Video footage shown on South Korean and Japanese media showed streets being cleared of traffic for a convoy of luxury vehicles, supposedly shuttling Kim through Beijing.
The meeting focused on Kim's expected meeting with Trump, according to Yonhap. "Judging from the delegation lineup, the mission appears to place emphasis on North Korea's continuing diplomatic outreach and nuclear and security issues", Aoki said.
Kim chose China for his maiden official trip overseas a year ago before holding meetings with South Korean President Moon Jae-in and Trump.
Tuesday was Mr. Kim's birthday. His visit is also seen as part of an effort to win Chinese support for a reduction of United Nations sanctions imposed over his nuclear weapons and ballistic missile programs that have severely impacted his country's already ailing economy.
Chinese Foreign Ministry spokesman Lu Kang would not comment on the objective or timing of Kim's visit at a briefing Tuesday, saying only that the two countries were making "joint efforts to uphold peace and stability on the Korean peninsula".More news: Roger Federer, Angelique Kerber cautious on new Australian Open tie-break rule