"We remain unchanged in our stance that (Kim's visit) will be possible and necessary before the end of this year", Baik Tae-hyun, a ministry spokesman, told a regular press briefing.
"The message is that President Trump has very favourable views toward Chairman Kim and he likes him", Mr Moon told reporters aboard a flight from Argentina to New Zealand, where he started a three-day state visit on Sunday.
When asked Saturday if he would ever host the North Korean leader in the United States, Trump replied: "At some point, yeah".
President Moon Jae-in (left) shakes hands with U.S. President Donald Trump on the sidelines of the G20 summit in Buenos Aires, Argentina on Friday. Kim agreed to travel to Seoul after hosting Moon in Pyongyang in September for their third summit this year. He said, "We are getting along very well".
The Trump-Kim summit in June of this year was created to help ease the tensions between the two nations - though critics have questioned whether North Korea has complied with agreements reached at the historic meeting.
The two leaders signed a document on disarmament but progress has since stalled as Washington and Pyongyang spar over what the agreement means.
The White House said in a statement on Saturday following Trump's meeting with Chinese President Xi Jinping that the US and North Korea would strive "to see a nuclear-free Korean Peninsula".
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It is also preparing hotels for the North Korean delegation to stay at when the possible visit to Seoul is confirmed.
Differences over how to denuclearize the North have kept the 2 countries from deciding the date and venue of the next summit.
The South's dovish President Moon has long favoured engagement with the nuclear-armed North and has dangled large investment and joint cross-border projects as incentives for steps towards denuclearisation.
-North Korea nuclear diplomacy, the AP reported.
Talks on a follow-up to the two leaders' first meeting in June in Singapore have been underway since July, a senior USA official told Reuters in October.
"North Korea summit", Moon said, adding Kim's trip to South Korea is still possible in December, although it depends on his decision.