Donald Trump, meanwhile, wrote on Twitter that another meeting with Kim "would be good in that we fully understand where we each stand".
In remarks carried earlier on Saturday by the official Korean Central News Agency, Mr Kim said he wouldn't welcome a repeat of the Hanoi summit in February, when Mr Trump walked out without securing a nuclear disarmament deal.
Kim said the United States "is further escalating the hostility to us with each passing day despite its suggestion for settling the issue through dialogue".
Telling North Korea's Supreme People's Assembly that USA diplomats came to the last meeting, which ended abruptly in late February with no agreement, without "a clear direction and methodology", Kim had tough words for the Trump administration in his speech Friday.
Since early 2018 Kim has embarked on a push for economic development and global engagement, including historic summits with the leaders of the United States, China and South Korea.
Kim said the United States is hinting at holding a third DPRK-U.S. Summit, but what happened in Hanoi "is not inviting" to the DPRK.
"However, the USA has taken a more hard-line stance since the Hanoi summit".
"Kim Yong Chol, the North's top nuclear negotiator, also has been sanctioned by Washington since 2010", Ahn Chan-il, the president of the World Institute for North Korea Studies in Seoul, told AFP.
Kim also said he wouldn't necessarily be focused on a summit to obtain sanctions relief and wouldn't hesitate to reach an agreement if the US brings up an idea that is acceptable to both sides, the report said.
Moon said it's important to maintain the "momentum of dialogue" and express a positive outlook to the global community that a "third U.S".
The failed face-to-face talks with President Donald Trump raise doubt whether the United States is really committed to improving relations with North Korea, its leader Kim Jong-un said, while promising to beef up the nation's defense.
Negotiations on Pyongyang's nuclear program appear to be stalled, and there is uncertainty over whether Kim is considering backing out of talks or restarting nuclear and missile tests.
Mr Kim said the United States had been refusing to withdraw what the North perceived as "hostile policies" while sticking to "mistaken judgment that we would succumb to maximum pressure". Kim held three summits previous year with Moon, who lobbied hard to revive the nuclear talks between the United States and North Korea.
"I'd like to express my high regard for how you have continued to express your trust towards Chairman Kim", Moon said. "The possibility for a North-South summit is decreasing and there will be limited outcomes, if any".
He also set the U.S. a deadline of "until the end of this year" to demonstrate that new talks could be more productive.
But, he added, "at this moment, we're talking about the big deal".
Following the collapse of the Trump-Kim summit, the North had been urging the South to break away from Washington and proceed with inter-Korean economic projects that are now held back by USA -led sanctions against the North.
In the months since Hanoi, there have been no known follow-up negotiations between Washington and Pyongyang.
Sanchez back in United squad for Barca clash
Sometimes it is luck, sometimes it is David at the other end saving. "We didn't stamp our authority on the game at home", the Norwegian added. "We know we need to perform better and play ourselves".
IPL 2019: Delhi Capitals beat Kolkata Knight Riders by 7 wickets
Ishant knocked out the off-stump of Joe Denly with a fantastic inswinger, the Englishman lasting just one ball on his IPL debut. They have now registered their 4th win of the season and moved to the 4th spot in the table surpassing KXIP due to better NRR.
NYC measles and mandatory vaccinations
Most of the reported cases are coming from people who have not been vaccinated or who do not know if they were vaccinated. Currently, New York's MMR vaccination rate is at 91.1 percent, below the 94 percent requirement to achieve herd immunity.
AA passenger jumps from grounded plane on runway in Arizona
While waiting for the main door of the plane to open, the man opened a service door on the other side of the plane and jumped out. The man was taken into custody without incident, police said, and was taken to a local hospital to treat his injuries.