The two met in an unannounced summit on Monday and Tuesday, in the port city of Dalian in China, just weeks after they took part in historic talks in Beijing.
According to China’s official Xinhua agency, Mr Kim and Mr Xi discussed bilateral issues, and the Chinese leader voiced his support for upcoming talks between North Korea and the US.
Mr Kim told Mr Xi he hoped relevant parties would take “phased” and “synchronised” measures to realise denuclearisation and lasting peace on the Korean peninsula.
He was quoted as saying his country was committed to denuclearisation if a “relevant party” dropped “hostile policy and security threats” – a thinly-veiled reference to the USA.
He was also quoted as saying: “I hope to build mutual trust with the US through dialogue.”
Mr Xi reportedly hosted a banquet, and state broadcaster CCTV showed the two leaders taking a seaside stroll.
According to Xinhua, Mr Xi said: “After the first meeting between me and Comrade Chairman (Kim), both China-DPRK relations and the Korean peninsula situation have made positive progress. I feel happy about it.”
Mr Kim is quoted as saying: “These are the positive outcomes of the historic meeting between me and Comrade General Secretary (Xi).”
North Korea state media said Mr Kim had told Mr Xi to continue their close relationship.
He also praised their high-level exchanges and said he was “very pleased” their relationship is reaching a high point.
Xinhua called the meeting “cordial and friendly” and said the two strolled by the sea at a government guesthouse before having lunch together on Tuesday.
CCTV quoted Mr Xi as saying China “supports North Korea to stick to denuclearisation of the Korean Peninsula and supports North Korea and the US in solving the peninsula issue through dialogue and consultation”.
Donald Trump tweeted he would be speaking to Mr Xi today.
I will be speaking to my friend, President Xi of China, this morning at 8:30. The primary topics will be Trade, where good things will happen, and North Korea, where relationships and trust are building.
— Donald J. Trump (@realDonaldTrump) May 8, 2018
The US President said: “I will be speaking to my friend, President Xi of China, this morning at 8:30. The primary topics will be Trade, where good things will happen, and North Korea, where relationships and trust are building.”
A summit is planned between Mr Trump and Mr Kim, but no date has been confirmed.
The US has said North Korea must commit immediately to getting rid of nuclear weapons.
China is North Korea’s only major ally but trade has plummeted in recent months because Beijing is enforcing UN economic sanctions, following ballistics missile tests in North Korea.
The unannounced meeting is Mr Kim’s second to China since March, and suggesting China does not want to be left outside while North Korea holds historic summits with South Korea’s President Moon Jae-In.
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It is not clear when the meeting was planned or put together or why Dalian was chosen. Mr Kim’s presence wasn’t confirmed until he left, flying out on Tuesday afternoon.
According to sources at the South China Morning Post, Mr Xi had flown to Dalian to preside over the official launch of sea trial for China’s first entirely self-built aircraft carrier.