The talks yielded an agreement to organize a meeting between the leaders of the two Koreas.
"Without US support and agreement, it will be hard to follow through on inter-Korean agreements". "If they can't, they should meet again to sign the treaty".
After U.S. President Donald Trump accepted Kim's proposal to hold the first-ever summit between the two countries, Kim headed to Beijing in late March to hold talks with Chinese President Xi Jinping, the first known time he met the head of a foreign government.
North Korean leader Kim Jong Un likely chose to put his nuclear weapons program up for negotiation to win outside rewards so he can improve his country's economy, win public trust at home and prolong his leadership, a special adviser to the South Korean president said Tuesday. Some experts say harsh United Nations sanctions or fears of US strikes could have driven Kim to initiate the peace offensive.
But Kim has changed course since the beginning of the year, sending a delegation to the Winter Olympics held in South Korea in February and agreeing to discuss with South Korea and the United States a nuclear program the North has defended as a necessary deterrent against U.S. invasion.
Seoul has said the peace treaty should be signed by the two Koreas, guaranteed by the U.S. and China with support from Russian Federation and Japan, and later approved by the UN.More news: Kendrick Lamar wins the Pulitzer Prize for music
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The Chinese side will make a final decision after observing the results of the planned US-North summit, according to the Yomiuri.
Mr Moon hopes that his summit with Mr Kim can lay the foundation for a deal on denuclearisation between Washington and Pyongyang at the following summit between Mr Kim and U.S. president Donald Trump in May or early June.
The April 27 summit between South Korean President Moon Jae-in and Kim is scheduled to take place in the border village of Panmunjom.
The recent thaw between Seoul and Pyongyang follows months of soaring tensions as the North conducted its most powerful nuclear test and launched more than 20 missiles - including two intermediate-range weapons that flew over Japan and another long-range missile that experts say puts the whole of the United States in striking distance.
The South Korean presidential chief of staff, Im Jong-seok, said on Tuesday that discussions will focus on fundamental issues - denuclearizing North Korea, establishing permanent peace on the Korean Peninsula and improving inter-Korean ties.
The two Koreas will hold working-level talks on Wednesday to discuss details such as protocol and security before holding another high-level meeting to prepare for the summit.