Mr Kim was expected to have sought China's help with getting relief from the sanctions during his visit. A motorcade including sedans, minibuses, motorcycles and a stretch limo with a golden emblem was seen leaving the airport.
Aviation sources said that Air Koryo's An-148 airplane were spotted taking off in Pyongyang early in the day and landing at Beijing's Capital International Airport at about 9:30 a.m.
The Koreas last held family reunions in 2015 before relations worsened because of North Korea's accelerated pursuit of nuclear long-range missiles and the hard-line response of Seoul's then-conservative government.
Moon's office said he made the remarks to Russian media ahead of his trip to Moscow later this week. The North Korean delegation led by Pak Thae-song, a close aide to Kim, met with top officials of Shaanxi Province.
Experts believe North Korea sees the "denuclearization of the Korean Peninsula" as something that would involve United States or South Korean concessions, including the possible removal of USA troops from the Korean Peninsula. "The Japan U.S. alliance plays a crucial role in this", Onodera said.
A series of posters celebrating the April 27 Panmunjom Declaration between Pyongyang and South Korea have also been released.
Kim leaves the North Korean Embassy in Beijing in this photo taken by Kyodo on Wednesday.More news: England World Cup game beats royal wedding in TV ratings
South Korea is hoping the talks will make possible regular contact between families long divided by the border, and broadcaster KBS reported that Seoul's delegation was planning to propose postal contact and hometown visits as potential measures.
United States President Donald Trump offered a misleading characterization of his deal with North Korean dictator Kim Jong Un on Thursday, insisting the nation had agreed to begin "total denuclearization" right away.
The suspension was an answer to Trump's announcement earlier this month of an end to U.S. military exercises in South Korea after his meeting with Kim, who committed to "complete denuclearization of the Korean Peninsula".
Ahead of this meeting, the USA quietly withheld nuclear assets from joint military exercises with South Korea in April and, later that month, Kim announced a freeze on all nuclear and longer-range missile tests before crossing the border to meet South Korean President Moon Jae-in.
"President Putin and I also share the common goal of completely denuclearizing the Korean Peninsula and establishing a peace regime", he said, according to Yonhap News Agency.
The two leaders had a candid and in-depth exchange of views on the current development of China-DPRK relations and the situation on the Korean Peninsula.
China and the USA both hope to see the Korean peninsula free of nuclear weapons, but Beijing is concerned Washington and Pyongyang might move closer at its expense, a possibility that China sees as threatening to its economic and security interests in the region.
South Koreans still vividly remember Trump's remarks at the United Nations in September of a year ago: "The United States has great strength and patience, but if it is forced to defend itself or its allies, we will have no choice but to totally destroy North Korea...."