Somerset - US President Donald Trump on Sunday mocked the leader of nuclear-armed North Korea as "Rocket Man" while White House advisers said the isolated nation would face destruction unless it shelves its weapons programmes and bellicose threats.Trump's chief diplomat held out hope the North would return to the bargaining table, though the president's envoy to the UN said the Security Council had "pretty much exhausted" all its options.Kim Jong Un has pledged to continue the North's programmes, saying his country is nearing its goal of "equilibrium" in military force with the US.North Korea will be high on the agenda for world leaders this coming week at the annual meeting of the UN General Assembly, Trump's biggest moment on the world stage since his inauguration in January.Trump is scheduled to address the world body, which he has criticised as weak and incompetent, on Tuesday.'Great threat'Trump, who spent the weekend at his New Jersey golf club, tweeted that he and South Korean President Moon Jae-in discussed North Korea during their latest telephone conversation on Saturday.Asked about Trump's description of Kim, national security adviser HR McMaster said "Rocket Man" was "a new one and I think maybe for the president".But he said: "That's where the rockets are coming from. Rockets, though, we ought to probably not laugh too much about because they do represent a great threat to all."McMcaster said Kim is "going to have to give up his nuclear weapons because the president has said he's not going to tolerate this regime threatening the United States and our citizens with a nuclear weapon".Asked if that meant Trump would launch a military strike, McMaster said: "He's been very clear about that, that all options are on the table."Some doubt that Kim would ever agree to surrender his arsenal."I think that North Korea is not going to give up its programme with nothing on the table," said Democratic Senator Dianne Feinstein of California, a member of the Senate Intelligence Committee.Kim has threatened Guam, a US territory in the Pacific, and has fired missiles over Japan, a US ally. North Korea also recently tested its most powerful bomb.Tougher US responseThe UN Security Council has voted unanimously twice in recent weeks to tighten economic sanctions on North Korea, including targeting shipments of oil and other fuel used in missile testing.Trump's UN ambassador, Nikki Haley, said North Korea was starting to "feel the pinch".Trump, in a tweet, asserted that long lines for gas were forming in North Korea, and he said that was "too bad".Secretary of State Rex Tillerson said he was waiting for the North to express interest in "constructive, productive talks"."All they need to do to let us know they're ready to talk is to just stop these tests, stop these provocative actions, and let's lower the threat level and the rhetoric," he said.But Haley warned of a tougher US response to future North Korean provocations, and said she would be happy to turn the matter over to Defence Secretary Jim Mattis "because he has plenty of military options".Mattis said after Kim tested a hydrogen bomb earlier this month that the US would answer any threat from the North with a "massive military response, a response both effective and overwhelming".Trump has threatened to rain "fire and fury" on North Korea if the North continued with its threats. Haley said that wasn't an empty threat from the president but she declined to describe the president's intentions."If North Korea keeps on with this reckless behaviour, if the United States has to defend itself or defend its allies in any way, North Korea will be destroyed and we all know that and none of us want that," Haley said."None of us want war. But we also have to look at the fact that you are dealing with someone who is being reckless, irresponsible and is continuing to give threats not only to the United States, but to all their allies, so something is going to have to be done."