At a time when "serious and complicated changes are happening in international and regional situations", KCNA said the two leaders agreed to "promote close strategic communication" and develop their "common interests".
US President Donald Trump statement comes days after he said he received a new "very warm" and "beautiful" letter from North Korean leader Kim Jong-un.
North Korean leader Kim Jong-un's half brother Kim Jong-nam was a spy for American intelligence, the Wall Street Journal reported, saying he was in Malaysia to meet his CIA handler in February 2017.
Kim and his wife were among the elite at the premiere of the games on Monday in Pyongyang, but North Korea's leader was unhappy with the event's organisers, state media said.
Can Russian President Vladimir Putin pick up where the US has failed in the Korean Peninsula?
How a crowd of 40,000 North Korean spectators put on a synchronised show, making marathon runners feel like professional athletes attending the opening ceremony of the Olympic Games.
Emulating his late father and grandfather, who took epic train trips when they were leaders, Kim set off on the long journey from Pyongyang, with a military honour guard seeing him off in the North Korean capital.
The announcement of Trump's second meeting with the reclusive North Korean leader came after the US President met at the White House for 90 minutes with a Pyongyang envoy, Kim Yong-chol, to discuss denuclearization talks.
North Korean leader Kim Jong-un and South Korean President Moon Jae-in visited Mount Paektu, considered sacred by Koreans, on the last day of Moon's visit for summit talks on the nuclear standoff and other inter-Korean affairs.
South Korean President Moon Jae-in is greeted with smiles and hugs by the North's leader Kim Jong-un ahead of a crucial summit over denuclearisation of the Korean peninsula and the prospect of officially ending the 1950-53 Korean War.
Hundreds of South Koreans will enter North Korea to reunite with their relatives and loved ones, as agreed by North Korean leader Kim Jong-un and South Korean President Moon Jae-in during their first summit in April.
A trip by the South's President Moon Jae-in to the North's capital would be the first such visit for more than a decade, as the diplomatic thaw on and around the peninsula builds.
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