In that historic summit, Trump and Kim opened up dialogue on the denuclearisation of the Korean peninsula after trading military threats for months.
"President Trump asked me to forward to [Kim] these messages; he has a very friendly view of Chairman Kim Jong Un and likes him".
Mr Trump added that at some point he would invite Mr Kim to the United States.
During the G20 summit, Trump met South Korean President Moon Jae-in and Japanese Prime Minister Shinzo Abe and agreed to stay firm in the application of sanctions on Pyongyang until it takes significant steps towards denuclearization.
Trump has said he hopes to meet with Kim early next year in a bid to give the talks a boost.
Mr. Trump had been in Buenos Aires for the Group of 20 summit.
"We're getting along very well".
Moon has facilitated a series of high-level talks between the USA and North Korea, including a summit between Trump and Kim in June, and has met Kim three times this year.
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The statement said Mr Xi and Mr Trump "agreed that great progress has been made with respect to North Korea".
On board is a team of South Korean experts investigating ways to help North Korea modernise its rail network.
Moon said a second summit between Kim and Trump will prove to be the "most critical moment" for North Korea's denuclearisation.
The pair "reaffirmed their commitment to achieve the final, fully verified denuclearisation" of North Korea, Mr Trump's spokeswoman Sarah Sanders said.
But the line has since then been put out of service due to heightened tension over the North's nuclear development programme.
U.S. President Donald Trump and North Korea's leader Kim Jong Un walk together before their working lunch during their summit at the Capella Hotel on the resort island of Sentosa, Singapore June 12, 2018.
But differences have emerged between Washington and Seoul on how to proceed with Kim, as the dovish Moon has long favored engagement with the North.
Prospects for a second summit to overcome a current logjam in negotiations will likely depend on whether either the USA or DPRK can show flexibility with regards to offering gestures surrounding sanctions relief or steps towards denuclearization.