By Heekyong Yang and Josh Smith

SEOUL (Reuters) - Kim Jong Un warned the United States on Monday he had a "nuclear button" on his desk ready for use if North Korea was threatened, but offered an olive branch to South Korea, saying he was "open to dialogue" with Seoul.

After a year dominated by fiery rhetoric and escalating tensions over Pyongyang's nuclear weapons program, the North Korean leader used his televised New Year's Day speech to declare his country "a peace-loving and responsible nuclear power" and call for lower military tensions and improved ties with the South.

"When it comes to North-South relations, we should lower the military tensions on the Korean Peninsula to create a peaceful environment," Kim said. "Both the North and the South should make efforts."

Kim said he would consider sending a delegation to the Winter Olympics Games in Pyeongchang, South Korea, in February.

"North Korea's participation in the Winter Games will be a good opportunity to showcase the national pride and we wish the Games will be a success. Officials from the two Koreas may urgently meet to discuss the possibility," Kim said.

South Korea said it welcomed Kim's offer. But U.S.-based experts saw Kim's speech as a clear attempt to divide Seoul from its main ally, Washington, which has led an international campaign to pressure North Korea through sanctions to give up weapons programs aimed at developing nuclear missiles capable of hitting the United States.

"We have always stated our willingness to talk with North Korea anytime and anywhere if that would help restore inter-Korean relations and lead to peace on the Korean Peninsula," a spokesman for the South Korean presidency said.

Lee Hee-beom, president of the Pyeongchang Organizing Committee, said it welcomed North Korean participation and would "discuss relevant matters with the South Korean government as well as the International Olympic Committee."

South Korean President Moon Jae-in has said North Korea's participation would ensure the safety of the Olympics and proposed last month that Seoul and Washington postpone large military drills that the North denounces as a rehearsal for war until after the Games.

Asked to comment on Kim's speech, U.S. President Donald Trump said: "We'll see, we'll see," as he walked into a New Year’s Eve celebration at his Mar-a-Lago resort in Florida.

'POKES AT THE FISSURE'

The U.S. State Department did not respond to a requests for comment on Kim’s New Year’s address, but analysts said it was an attempt to weaken the U.S.-South Korean alliance.

"This speech pokes at the fissure that has lain below the surface in U.S.-South Korean relations, and seems designed to drive a wedge there," said Douglas Paal, a former senior U.S. diplomat who heads the Asia program at Washington’s Carnegie Endowment for International Peace.

"President Moon needs a successful Olympics and the U.S. drive to increase pressure fits poorly with the Southern agenda."

Evans Revere, another former senior U.S. diplomat who took part in unofficial talks with North Korean officials last year, said Pyongyang would likely try to extract concessions as a “price” for Olympics participation.

"It’s hard to imagine Seoul falling for this," he said, adding that Seoul and Washington had so far stayed in synch in the pressure and isolation campaign.

Revere said Kim’s speech contained the strongest defense yet of North Korea's status as a permanently nuclear-armed country.

"Implicit in Kim Jong Un’s speech is a willingness to engage with others, including the United States, on the basis of their acceptance of the 'reality' of North Korea’s permanent nuclear status. That’s not a basis on which the United States is prepared to engage," he said.

Moon took office last May pledging to engage Pyongyang in dialogue. But North Korea snubbed his overtures, including an offer to hold inter-Korean military talks about ceasing hostile activities along the border, as it tested missiles at an unprecedented pace.

Kim said that rather than encouraging U.S. measures that "threaten the security and peace of the Korean peninsula," Seoul should instead respond to overtures from the North, and "stop nuclear war exercises with foreign forces."

'REALITY, NOT A THREAT'

North Korea conducted its sixth and most powerful nuclear test in September in defiance of international sanctions, raising fears of a new conflict on the Korean peninsula.

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