Image copyright Getty Images Image caption Residents of South Korea watched the speech from the North's leader 
 
 North Korea's leader Kim Jong-un has said a nuclear launch button is "always on my table" and warned the US it will never be able to start a war. 
 
 In a televised new year speech, he said the entire US was within range of North Korean nuclear weapons, adding: "This is reality, not a threat." 
 
 But he also offered a potential olive branch to South Korea, suggesting he was "open to dialogue". 
 
 He said the North may send a team to the Winter Olympics in South Korea. 
 
 What is President Trump's reaction? 
 
 When asked by reporters to respond to Mr Kim's latest threats, US President Donald Trump said, "We'll see, we'll see". 
 
 He was speaking at the sidelines of New Year's Eve celebrations at his Mar-a-Lago resort in Florida. 
 
 North Korea has come under increased criticism and sanctions over the past year because of its nuclear weapons programme and repeated testing of conventional missiles. 
 
 Media playback is unsupported on your device Media caption North Korea said in November its latest missile was capable of reaching Washington DC 
 
 It claims to have a fully deployable nuclear weapon, though there is still some international scepticism about its true capacity to carry out such an attack. 
 
 In his speech, Mr Kim re-emphasised his focus on the weapons programme, but implied the country still has a few stages left to go before achieving its ambitions. North Korea must "mass-produce nuclear warheads and ballistic missiles and speed up their deployment", he said. 
 
 He also said they would not use their weapons unless they felt that peace was threatened. 
 
 Thawing relations with the South? 
 
 While his language against the US remained tough, Mr Kim did not employ his typically antagonistic tone when speaking about his neighbours in South Korea. 
 
 "The year 2018 is a significant year for both the North and the South, with the North marking the 70th anniversary of its birth and the South hosting the Winter Olympics. 
 
 Image copyright Reuters Image caption Pyongyang's seasonal ice festival includes an ice sculpture of an intercontinental ballistic missile 
 
 "We should melt the frozen North-South relations, thus adorning this meaningful year as a year to be specially recorded in the history of the nation," he said. 
 
 A spokesperson for the South Korean president said their office had "always stated our willingness to talk with North Korea at anytime and anywhere". 
 
 "We hope the two Koreas will sit down and find a solution to lower tensions and establish peace on the Korean peninsula." 
 
 Youngshik Daniel Bong, a research fellow at Yonsei Institute for North Korean Studies, told the BBC that addressing the South was a marked change from the norm for Mr Kim. 
 
 "North Korea usually ignores South Korea, maintaining the position that as a 'nuclear power' it will deal with the US on its own," said Mr Bong. "It appears that by engaging the South, he hopes to create an estrangement between South Korea and the US." 
 
 The analyst also said that Mr Kim could be seeking to improve ties to offer some respite from the growing economic pressures from the recent UN sanctions. 
 
 Will North Korea now go to the Olympics? 
 
 Mr Kim also said he would also consider sending a delegation to the Games in Pyeongchang, South Korea, in February - a gesture which South Korea has previously suggested would be welcome. 
 
 "North Korea's participation in the Winter Games will be a good opportunity to show unity of the people and we wish the Games will be a success," he said. 
 
 "Officials from the two Koreas may urgently meet to discuss the possibility." 
 
 Image copyright Reuters Image caption Can sports and diplomacy mix on the ice with the presence of North Korea's figure skaters Ryom Tae-Ok and Kim Ju-Sik? 
 
 The president of the PyeongChang Games' organising committee, Lee Hee-beom, told South Korea's news agency Yonhap he was delighted to hear of the potential participation. 
 
 "[The committee] enthusiastically welcomes it. It's like a New Year's gift," he said. 
 
 The only two North Korean athletes who qualified for the Games are figure skaters Ryom Tae-Ok and Kim Ju-Sik. 
 
 Although the North has missed the official deadline to confirm their participation, the skaters could still compete with an invitation by the International Olympic Committee. 
 
 South Korea's President Moon Jae-in last month suggested delaying an annual joint military drill with US troops until after the Games. The North usually denounces any such exercises as a rehearsal for war. 
 
 Robert Kelly, a political science professor at South Korea's Pusan National University, told the BBC that the Winter Olympics statement was "a smart move from North Korea" as it positioned Mr Kim's regime as moving towards its neighbours while the US was seeking to isolate it. ||||| North Korean leader Kim Jong Un boasted in an annual New Year's Day speech Monday that he had a nuclear button on his desk and that the entire United States was within range of his weapons — but he also vowed not to attack unless threatened. 
 
 Kim promised to focus this year on producing nuclear warheads and missiles for operational deployment. But he also struck a conciliatory note, opening the door to dialogue with South Korea and saying he would consider sending a delegation to the Winter Olympics to be held in his southern neighbor in February. 
 
 "The United States can never fight a war against me and our state," he said in the nationally televised speech. "It should properly know that the whole territory of the U.S. is within the range of our nuclear strike and a nuclear button is always on the desk of my office, and this is just a reality, not a threat." 
 
 But Kim also said that North Korea was a peace-loving and responsible nuclear power, and would not use its nuclear weapons unless "hostile aggression forces" encroach on its sovereignty or interests. 
 
 "This year, we should focus on mass-producing nuclear warheads and ballistic missiles for operational deployment," Kim said. "These weapons will be used only if our security is threatened." 
 
 North Korea conducted its sixth and most powerful nuclear test in September and launched its most high-tech intercontinental ballistic missile in November, ignoring international condemnation and steadily tightening sanctions. 
 
 [Documents shed light on North Korea’s startling gains in sea-based missile technology] 
 
 In typically bellicose language, it declared the latest round of United Nations sanctions imposed last month an "act of war," and Kim said his country had achieved the historic feat of "completing" its nuclear forces. 
 
 North Korea's nuclear capabilities do not yet match Kim's boasts, experts say, since it is far from clear it could successfully deliver a nuclear weapon on one of its missiles. Yet there is little doubt its capabilities have advanced significantly in the past year. 
 
 But Kim, dressed in a Western-style gray suit and tie, also offered a potential olive branch to Seoul, saying it is imperative to lower military tensions on the Korean Peninsula and improve ties with the South. 
 
 He said that the path to dialogue was open and that he would consider sending a delegation to the Winter Olympics in Pyeong­chang, South Korea. 
 
 "North Korea's participation in the Winter Games will be a good opportunity to show unity of the people, and we wish the Games will be a success," he said. "Officials from the two Koreas may urgently meet to discuss the possibility." 
 
 South Korea has been trying to reassure the rest of the world that the Olympics will be safe despite the nuclear tensions, and President Moon Jae-in has said North Korea's participation would ensure their safety. He also proposed last month that Seoul and Washington postpone annual joint military drills until after the Olympics, and he generally takes a less-confrontational approach to relations with the North than his predecessor, Park Geun-hye. 
 
 John Delury, a professor of international relations at Yonsei University in Seoul, said Kim's message to Seoul was "more promising" than he had anticipated, addressing in a specific and actionable way South Korea's desire to make the Games a success. 
 
 "That should give hope to those in the South who are trying to get something going and open a channel at least," he said. 
 
 [U.N. imposes new sanctions on North Korea over missile tests] 
 
 The idea of improving relations between the two Koreas is one that is frequently spoken about but seldom achieved, and Kim's warmer words could also be seen as an attempt to drive a wedge between Seoul and Washington. 
 
 While Kim's words were more combative toward the United States, he also refrained from a personal attack on President Trump, after the two men engaged in several rounds of mutual name-calling in 2017, Delury noted. 
 
 When asked about North Korea's nuclear claims Sunday night, Trump said only, "We'll see, we'll see." 
 
 Daryl Kimball, executive director of the Arms Control Association, said Kim's claims about his country's nuclear capability underscored that there was no viable "military solution" to denuclearizing North Korea and that sanctions alone would not persuade Pyongyang to halt or reverse its nuclear buildup. 
 
 "To avoid a nuclear conflict and the full-scale deployment of an operational North Korean strategic deterrent force, U.S. leaders, in concert with South Korea, should redouble efforts to engage North Korea in direct talks and cease any further explicit or implicit threats of military action against the North," he said in an email. 
 
 "The upcoming Olympics provide an important opportunity to break the ice and to begin discussions with the North Koreans on mutual steps that reduce the chances of miscalculation and war," he added. 
 
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– Kim Jong Un's New Year's Day speech is being widely described as an "olive branch"—despite the fact that he warned the nuclear button is "always on his table" and bragged that the entire US is now within the range of his country's nuclear weapons. "This is reality, not a threat," the North Korean leader said, though he also said he was "open to dialogue" with South Korea and suggested his country might send a delegation to the Winter Olympics being held in the South next month, the BBC reports. He said North Korea will focus on mass-producing nuclear weapons and ballistic missiles in 2018, but these "weapons will be used only if our security is threatened." "We should melt the frozen North-South relations," Kim said, adding that the "Winter Games will be a good opportunity to show unity of the people, and we wish the Games will be a success." John Delury at Seoul's Yonsei University tells the Washington Post that Kim's words "should give hope to those in the South who are trying to get something going and open a channel at least." He says Kim may be trying to drive a wedge between Seoul and Washington, though the fact that the North Korean leader refrained from insulting President Trump may be a good sign. Asked about Kim's "nuclear button" remarks by reporters at the Mar-a-Lago New Year's Eve party, Trump said "We'll see."