'The message is that president Trump has very favourable views toward Chairman Kim and he likes him, ' Moon told reporters aboard a flight from Argentina to New Zealand, where he started a three-day state visit on Sunday.
"President Trump asked me to forward to [Kim] these messages; he has a very friendly view of Chairman Kim Jong Un and likes him".
Speaking in Buenos Aires, where he discussed the situation on the Korean Peninsula with Mr Moon, Mr Trump said he hoped to organise a follow-up meeting with Mr Kim for early next year.
According to several Western media outlets, Trump told them aboard Air Force One after attending the Group of 20 (G20) summit that the meeting would occur early in 2019.
"There is a possibility that Chairman Kim Jong-un's visit to Seoul may be made within this year, but there's more important things than the timing", he said in translated remarks during a visit to New Zealand.
Kim sharply raised tensions with nuclear and missile tests last year, but suddenly reached out to South Korea and the United States this year with a vague nuclear disarmament pledge. Despite the warming ties, it remains unclear whether Kim will make his first-ever visit to the South this year, as Seoul is hoping.More news: Cricket star Usman Khawaja's brother Arsalan reportedly arrested over terror hit list
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President Moon Jae-in is calling on South Korea and Japan to cleverly handle their uncomfortable history, ... and secure future-oriented relations that are not affected by what happened in the past.
"We have actually talked about three sites, we haven't determined the sites", he said. Their two previous summits were held at the countries' shared border village of Panmunjom.
Ardern said New Zealand will soon allow smoother immigration procedures for visitors from South Korea and plans to improve pension portability between the two countries.
Moon's programme in Auckland includes a ceremony of welcome and a state lunch hosted by Governor-General Dame Patsy Reddy at Government House, a wreath laying ceremony and tour of Auckland War Memorial Museum, and an engagement with the Korean community in Auckland. Subsequent nuclear diplomacy hasn't made headway since the US-North Korea summit in June.
They agreed on the need for "maintaining vigorous enforcement of existing sanctions to ensure the DPRK understands that denuclearization is the only path", Sanders said, using the North's official name, the Democratic People's Republic of Korea.
Trump signalled on Saturday he was likely to meet Kim again in January or February.