"We have a good relationship", Trump told reporters aboard Air Force One on his return trip from the G-20 summit in Argentina, adding he would invite Kim to the United States "at some point", according to Reuters.
"I think we're going to do one fairly (soon) - into January, February, I think", Trump said in remarks carried by the AFP news agency.
Former UN Secretary-General Ban Ki-moon urged North Korean leader Kim Jong Un on Monday to take concrete steps toward complete denuclearisation and gain the trust of the worldwide community if he wants sanctions lifted.
North Korea is seeking security guarantees from the United States and relief from worldwide sanctions.
However, North Korea has taken steps to cease its ballistic missile and nuclear programs. The former South Korean foreign minister said on Monday "this is the time" to achieve Pyongyang's denuclearization after almost a quarter century of unsuccessful efforts, adding that the North and the world should not lose this opportunity. "I'd like to really advise the North Korean leader that the world is ready" to help his country, Ban told AP, specifically citing South Korea, the US, China, Japan and Russian Federation.
They agreed on the need for "maintaining vigorous enforcement of existing sanctions to ensure the DPRK understands that denuclearisation is the only path", Sanders said, using the North's official name, the Democratic People's Republic of Korea.
The South Korean government is optimistic over Kim's visit to Seoul, which he promised during the third inter-Korean summit in September in Pyongyang.
They have also begun work to reconnect a train line and fix another rail link across the border.
Trump "hopes for Chairman Kim Jong Un to fulfill the rest of his agreements, and said he will grant what Chairman Kim Jong Un wants", Moon told reporters.
The two leaders said Kim's visit to the South Korean capital "would provide additional momentum to their joint efforts to establish peace on the Korean peninsula", Moon's press secretary Yoon Young-chan said.
Moon said he and Trump agreed during their meeting that Kim's trip to Seoul would play a "very positive role" in U.S.
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