Lavrov's visit to Kim comes as Secretary of State Mike Pompeo is meeting with a senior North Korean official in NY, where they tried to work through recent problems to get the USA and North Korea back on track for a June 12 summit between President Trump and Kim in Singapore.
High-ranking officials of the US and North Korea have met in NY in the first of two days of talks about the future of Pyongyang's nuclear weapons programme and a possible summit between US President Donald Trump and leader Kim Jung Un.
When asked about the working dinner, Pompeo told reporters afterwards: "It was great".
Trump had been scheduled to meet Kim in Singapore on June 12, but the meeting was thrown into doubt after the USA leader said he was cancelling it.
It was not yet known whether they made any progress toward narrowing long-standing differences between Washington and Pyongyang that could end decades of hostile relations.
The talks, which are the most critical of three tracks of negotiations now taking place between the two governments in the United States, in the heavily fortified Korean Demilitarised Zone, and in Singapore - are aimed at determining whether a meeting between Mr Trump and Kim Jong Un can be restored.
The talks come as preparations for the highly anticipated summit in Singapore were barrelling forward both in the US and in Asia, despite lingering uncertainty about whether it will really occur, and when. He said North Korea will never agree to have its complete nuclear weapons packed up and shipped out of the country.
Conveying a message from Russian President Vladimir Putin, Lavrov said the Kremlin wished Kim "success in those major undertakings that are now initiated on the Korean Peninsula with your participation".
Nonetheless, in a surprise meeting earlier this week, Kim and South Korean President Moon Jae-in affirmed their shared goal of achieving complete dismantlement of the North's nuclear, chemical and biological weapons and ballistic missile programs, according to a statement.
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U.S. officials have also met North Korean envoys in Panmunjom on the inter-Korean border, while more USA diplomats have arrived in Singapore to prepare for the event. North Korea and the United States are still technically at war and have no diplomatic ties because the 1950-53 Korean War ended with an armistice, not a peace treaty. Until recently, the North has viewed South Korea and the U.S.as its adversaries.
Mr. Clinton's secretary of state, Madeleine Albright, later visited the North Korean capital, but the negotiating effort eventually collapsed.
At the White House, press secretary Sarah Huckabee Sanders gave an upbeat assessment of preparations for the summit and said the United States is "shooting for" a reinstatement of the meeting as scheduled on June 12. "It will not be easy to narrow the gap and find common ground but I think it would not be impossible".
In return the U.S. was offering "the security guarantees they feel they need" and help for North Korea to achieve greater prosperity.
Kim Jong-chol, who many in South Korea hold responsible for a torpedo attack on the South Korean corvette Cheonan, which killed 46 sailors in 2010, is the harder-edged of the two.
Russian Foreign Minister Sergei Lavrov met North Korean leader Kim Jong Un in Pyongyang on Thursday, the Russian foreign ministry said, and invited him to visit Russia.
Lavrov began his visit to North Korea by meeting with Foreign Minister Ri Yong Ho.
North Korea will try to maintain its nuclear program in some capacity, said Ralph Cossa, president of the Pacific Forum at the Center for Strategic and International Studies.
Thursday's meeting between Kim and Lavrov took place at the Paekhwawon State Guest House in Pyongyang, the Kremlin-run TASS news agency reported quoting a source in the Russian delegation.
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