But Kim did not mention denuclearisation at any point in his remarks, and it was Moon who communicated the North's plans to close the Yongbyon nuclear reactor as well as shut missile test pads in front of "international experts".
It was unclear what those "reciprocal steps" would be.
South Korean President Moon Jae-in and North Korean leader Kim Jong Un announced a sweeping set of agreements after their second day of talks in Pyongyang on Wednesday that included a promise by Kim to permanently dismantle the North's main nuclear complex if the United States (US) takes corresponding measures, the acceptance of global inspectors to monitor the closing of a key missile test site and launch pad and a vow to work together to host the Summer Olympics in 2032.
At the start of their meeting Tuesday, Kim thanked Moon for brokering the June summit with Trump.
Those U.S. steps could include an end-of-war declaration, South Korea's national security adviser, Chung Eui-yong, told reporters.
The Koreas also agreed to work toward easing military tensions on the Korean peninsula, increasing communication and cooperation and facilitating more family reunions.
North Korean Defense Minister No Kwang Chol and South Korean Defense Minister Song Young-moo signed a military agreement to implement the Panmunjom agreement.
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Speaking at a joint press conference with South Korea's President Moon Jae-in on Wednesday, North Korean leader Kim Jong Un also said he will visit the South's capital Seoul "in the near future".
Seoul officials hope Moon will be able to convince Trump to restart nuclear talks with Pyongyang, after he canceled a trip by his secretary of state to Pyongyang last month, citing lack of progress.
The South's delegation's was served lunch at Okryugwan, a Pyongyang restaurant famous for its cold noodles.
On Wednesday evening, Moon and his party will have dinner at the newly-opened Taedonggang fish restaurant on the banks of the eponymous river that flows through Pyongyang.
A farewell dinner banquet is to follow. Seoul officials said they did not expect any specific joint economic projects to be agreed given global sanctions.
On the front, there was a photo of the two leaders shaking hands and hugging each other upon meeting at Pyongyang International Airport on Tuesday, with more inside of them parading together through the streets of the city, enjoying a concert and toasting at a banquet.
Mr. Moon is also scheduled to watch the North's signature "Brilliant Fatherland" Mass Game which was reintroduced this year following a five-year hiatus, with a formation of glowing drones, lasers and stadium-sized gymnastics shows created to glorify the country.
The dinner banquet that followed was amicable throughout the whole three hours, officials said, with it wrapping up past 11 p.m.