President Donald Trump said sanctions have started having "a big impact" on North Korea and its leader, whom he calls "Rocket man."

"Soldiers are dangerously fleeing to South Korea. Rocket man now wants to talk to South Korea for first time," Trump tweeted Tuesday. "Perhaps that is good news, perhaps not - we will see!"

Kim's comments appear to have galvanized efforts within Moon's administration to secure North Korea's participation in the Games.

On Tuesday, South Korean Unification Minister Cho Myoung-gyon suggested high-level government talks with North Korea could be held as soon as January 9 in the border village of Panmunjom in the Demilitarized Zone.

"The government proposes the North to hold high-level, inter-Korean government talks at the Peace House of Panmunjom in consideration that the Winter Olympics is about a month away and to discuss related matters such as the participation of North Korea's delegation in the Pyeongchang Olympics," Cho said during a press briefing in Seoul.

Cho added his government would remain "open to suggestions" as to the "timing, venue and format" of any future dialogue with the North.

When asked for her reaction to the potential upcoming talks between the two countries, US Ambassador to the United Nations Nikki Haley said Tuesday the United States won't take any North Korea talk seriously "if they don't do something to ban all nuclear weapons in North Korea."

North Korea has yet to respond to the South's offer. Indeed, it has long been difficult to reach North Korea for direct communication, the South's Unification Ministry says.

Since then, the ministry has called the North on the hotline twice a day, Monday through Friday, but the North has not answered, the spokeswoman said. That includes two unanswered calls on Tuesday, a day after Kim's message, she said.

Nevertheless, China's Ministry of Foreign Affairs welcomed the efforts from both the North and South to improve relations.

The Games are due to take place 30 years after Seoul hosted the Summer Olympics, a turbulent era in which a number of nations -- including North Korea -- boycotted the event.

There has been talk of the International Olympic Committee granting an additional quota, something previously proposed by Choi Moon-soon, governor of the Gangwon province that will host the Winter Games.

Follow-up measures

Kim's sudden willingness to reach out to the South has surprised analysts, leading to suggestions it may be part of a strategy to drive a wedge between Seoul and Washington.

Rodger Baker, vice president of strategic analysis for the intelligence firm Stratfor, told CNN that Kim may be seeking to "exploit Seoul's sense of insecurity" by enlisting it in pushing back against tighter US containment.

Moon's stance has been compared to the so-called Sunshine Policy of the liberal governments of 1998 to 2008. Under it, Seoul actively engaged Pyongyang, which led to closer relations and saw two South Korean leaders visit the North Korean capital. However, the approach failed to halt North Korea's nuclear weapons program.

Speaking Monday, Moon said improvements in inter-Korean relations was "not a matter that can go a separate way from the issue of resolving the North Korean nuclear issue."

"I also ask the Foreign Ministry to closely consult with our allies and the international community to push for both an improvement in inter-Korean relationship and the resolution of the North Korean nuclear issue at the same time," he said.

Tong Zhao, a fellow at the Carnegie-Tsinghua Center in Beijing, told CNN that North Korea does "not want to appear threatening and provocative."

"He (Kim) wants to convince the international community that his nuclear weapons are purely for self-defense and wants to have a negotiated solution with the United States on the basis that he gets to keep its nuclear deterrent capability," he said.

"After achieving a preliminary strategic deterrent capability, North Korea might want to de-escalate tensions and see(s) the Winter Olympics as a golden opportunity. The Games make it possible for Washington and Seoul to meet Pyongyang's demand for self-restraint -- adjusting their military exercises -- without losing face and appearing weak on Pyongyang."