In last week's summit with Trump, the US leader also asked Moon to inform him about the North's position after any inter-Korean contact, suggesting that an upcoming inter-Korean summit, if it takes place, will address a more specific nuclear deal to be used in a possible Kim-Trump summit later.
The warning comes after Kim Jong-Un said he would only agree to further talks at a third summit if the US has the "right attitude". Kim said in the speech that he is willing to try a third summit with Trump, but only if the United States changes its approach.
The U.S. president responded to Kim's statement on Twitter. "The big deal is we have to get rid of the nuclear weapons", Trump explained.
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. Moon's call for partial sanctions relief to create space for the inter-Korean projects and induce nuclear disarmament steps from the North has caused disagreements with Washington, which sees economic pressure as its main leverage with Pyongyang.
Trump and Kim held their first landmark summit in Singapore last June, where they signed a vaguely-worded agreement on the "denuclearisation of the Korean peninsula".
North Korea has held a series of sports and cultural events over the past few days.
"Chances are fairly high that a summit between Russian Federation and North Korea could take place around that time", the news agency said.
Kim blamed the collapse of his second summit with Trump on what he described as Washington's unilateral demands.
"In his speech after being re-elected as the State Affairs Commission chairman, Kim once again declared his strong determination for the denuclearization of the Korean Peninsula and the establishment of peace", Moon said.
The United States is "is still shunning the withdrawal of its hostile policy, the fundamental way of establishing the new DPRK-U.S. relations, and miscalculating that it can bring us to our knees if it puts maximum pressure on us", Kim said.
Although they described the exercises as defensive in nature, the United States and South Korea have downsized the drills to create a space for diplomacy with North Korea, which sees them as invasion rehearsals.
"Now the North is turning its eyes to Russia", Park said.