Mr. Moon has repeatedly called for dialogue with the North, hoping that talks would ease tensions and lead to broader international negotiations to end its nuclear weapons program.
Hours after Mr. Kim’s speech, Mr. Moon’s office welcomed the North’s proposal.
“We have already expressed our willingness to engage in a dialogue with North Korea at any time, in any place and in any format, as long as both sides can discuss restoring their relations and peace on the Korean Peninsula,” said Park Soo-hyun, Mr. Moon’s spokesman.
Mr. Trump, on the other hand, has stressed maximum pressure and sanctions, and even suggested possible military action to force the North to give up its nuclear arsenal.
Mr. Moon officially supports the enforcement of United Nations sanctions. In recent weeks, his government has seized two oil tankers on the suspicion that they were used in violation of the sanctions to smuggle refined petroleum products into North Korea through ship-to-ship transfers on the high seas.
But the South Korean president also agrees with China and Russia that talks are needed to resolve the nuclear crisis. Mr. Kim’s sudden peace overture on Monday will probably encourage both South Korea and China to raise their voices for dialogue.
“Kim Jong-un is using the Pyeongchang Olympics as a way to weaken the sanctions,” said Kim Yong-hyun, a professor of North Korean studies at Dongguk University in Seoul. “He is seeking to create a fissure between Seoul and Washington and between Washington and Beijing.”
In his speech, Mr. Kim warned that he had “a nuclear button” in his office that could send intercontinental ballistic missiles, ICBMs, hurtling toward any point in the mainland United States. He also vowed to increase production of nuclear-capable missiles.
On Nov. 29, when the North launched an ICBM with engines powerful enough to send a warhead to the East Coast of the United States, North Korea already claimed to have completed its nuclear arsenal.
Analysts have said that the North has yet to master the missile technology needed to protect a nuclear warhead when it re-enters the earth’s atmosphere from space. They said that despite the North’s claim to have completed its weapons program, the regime was likely to conduct more weapons tests to improve its capabilities.
But in addition to improving its weapons technology, the North also wants to ease crippling sanctions that limit fuel supplies and hard currency entering the country.
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In recent years, while ignoring South Korea, North Korea has pursued opportunities for talks with Washington. But those efforts have not created a long-term solution.
The United States is not interested in holding talks that lack a clear commitment from the North to discuss denuclearization. The North, however, insists on being recognized as a nuclear state.
“After getting nowhere with the Americans, North Korea is now trying to start talks with South Korea first and then use that as a channel to start dialogue with the United States,” said Yang Moo-jin, a professor at the University of North Korean Studies in Seoul.
The isolated North made major strides last year in its nuclear weapons program. On Sept. 3, it detonated what it called a hydrogen bomb in its sixth and most powerful nuclear test. It has also launched three intercontinental ballistic missiles in the past year.
But the country has also faced harsh sanctions from the United Nations Security Council. The Council has sought to squeeze North Korea’s main sources of foreign currency by banning its exports of coal, iron ore and sea products and curtailing the employment of North Koreans in other countries. It has also demanded that member nations drastically reduce exports of refined oil to North Korea.
While gas prices in the North more than doubled in 2017, analysts said the country could feel more pain this year, depending on how stringently the sanctions are enforced, especially by China, the North’s primary trading partner.
Hard-liners in South Korea and the United States fear that if dialogue on the Korean Peninsula creates a temporary reprieve from tensions, the enforcement of sanctions could also be relaxed. Officials in the Moon administration said that they were aware of the North’s strategy and that they closely coordinate their moves with Washington.
For Mr. Moon, the inter-Korean talks would provide a badly needed respite after a year in which Mr. Kim and Mr. Trump regularly exchanged threats of war. Mr. Trump has said he could unleash “fire and fury” and “totally destroy North Korea,” while North Korea has suggested it could conduct a hydrogen bomb test over the Pacific.
Increasingly anxious over a possible armed conflict, Mr. Moon seeks to create a lull in the nuclear standoff during the Olympics and use its momentum to start talks with North Korea. Such talks, he hopes, might eventually lead to broader negotiations in which the United States, China and other regional stakeholders could offer economic and diplomatic incentives to the North in return for the freeze and eventual dismantling of its nuclear weapons program.
Last month, Mr. Moon proposed that South Korea and the United States postpone joint military exercises that were expected to start in February if North Korea suspended weapons tests in the weeks leading up to the Olympics.
Analysts said that in any future talks North Korea would seek major concessions, like the easing of sanctions and a reduction of the American military presence on the Korean Peninsula. In return, the North would probably try to force Washington to accept a compromise by offering to freeze or give up its ICBMs, while keeping other nuclear assets as leverage.
On Monday, Mr. Kim urged South Korea to cease joint military exercises with the United States, adding that the Americans would never dare start a war with North Korea.
Cheong Seong-chang, a senior analyst at the Sejong Institute, a South Korean think tank, said: “In this year’s New Year’s Day speech, he is more confident than ever about a nuclear deterrent against the United States. It is based on that confidence that he is proposing to improve ties with South Korea.”