Departing for a trip to Iowa, Trump told reporters at the White House that he still has a "very good relationship" with the North Korean leader and "appreciates" receiving the latest letter.
During a visit to Oslo, Moon said it was "desirable that Chairman Kim and President Trump meet in the near future".
South Korean officials said Kim Yo Jong, who has emerged over the past 18 months as a top aide to her brother, did not have any particular message or letter for South Korean President Moon Jae-in. Trump added that he had seen the "information about the Central Intelligence Agency in regard to his brother or half-brother, and I would tell him [Kim Jong-un] that would not happen under my auspices". Fifield says Kim Jong Nam usually met his handlers in Singapore and Malaysia, citing a source with knowledge of the intelligence.
Responsibility for that murder has been laid directly at the feet of Kim Jong-un, and yesterday The Wall Street Journal reported on what may have been the motive for the murder. Bolton said to the Wall Street Journal on Tuesday, "We are ready whenever they want". He is due to travel to Japan and South Korea later this month.
Early optimism that the leaders' personal rapport would lead to a deal on denuclearisation weakened after their most recent talks ended without an agreement and competing accounts of why the summit ended in disarray. "I think North Korea has tremendous potential".
Pyongyang has called on Seoul to implement joint economic projects agreed a year ago at inter-Korean summits, but sanctions imposed on the North over its nuclear and ballistic missile programmes have blocked progress.
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Though Trump's two meetings with Kim Jong Un signaled the first-ever between a sitting US president and North Korean ruler, Moon too has made history with a record three inter-Korean summits, the first of which saw Kim Jong Un become the first in his position to cross the border.
North Korea has chronic energy shortages, and satellite images of the peninsula at night illustrate the problem by showing a brightly lit South Korea and an nearly completely dark North Korea, formally known as the Democratic People's Republic of Korea.
Kim was assassinated at Kuala Lumpur International Airport in 2017 when two women smeared his face with what appeared to be a nerve gas.
Kim Hyo-sun has this report.
After North Korea's projectile tests, Kim had some bad news for her South Korean counterpart.
But, North Korean officials continue to say the exact opposite, warning they will not give up their weapons unilaterally and setting an end-of-the-year ultimatum for the United States to change its approach.