Washington, Oct 2: The President of the US said on Sunday that his secretary of state was wasting his time trying to negotiate with North Korea. Donald Trump made his remarks after Rex Tillerson had said in a press conference Saturday in Beijing that the US had established direct channels with the secretive Asian nation and was seeking to calm tensions related to its defiant pursuit of a nuclear programme, Efe reports. "I told Rex Tillerson, our wonderful Secretary of State, that he is wasting his time trying to negotiate with Little Rocket Man," Trump tweeted, using his nickname for North Korean supreme leader Kim Jong-un. "Save your energy Rex, we'll do what has to be done!" Trump added. Tillerson said in Beijing that US officials were probing Pyongyang's willingness to engage in dialogue, although he did not specify the nature of those overtures or whether they were being made via Chinese authorities. Shortly afterward, State Department spokeswoman Heather Nauert issued a statement in Washington reiterating the existence of "several open channels." "(But) despite assurances that the United States is not interested in promoting the collapse of the current regime, pursuing regime change, accelerating reunification of the peninsula or mobilizing forces north of the DMZ, North Korean officials have shown no indication that they are interested in or are ready for talks regarding denuclearisation," she added. Tillerson's announcement came amid a sharp increase in tensions triggered by North Korea's latest nuclear test (of a hydrogen bomb) last month and heated rhetoric by both Trump and North Korean officials. Trump ominously warned Pyongyang on in his debut speech before the United Nations General Assembly on Sept. 19 that the US would obliterate the Asian country if necessary. "The United States has great strength and patience, but if it is forced to defend itself or its allies, we will have no choice but to totally destroy North Korea," Trump said in his UN speech. Two days later, Kim accused Trump of being mentally deranged and said he would "pay dearly" for making threats against North Korea. The Asian nation's foreign minister, Ri Yong-ho, told reporters in New York on Sept. 22 that North Korea may retaliate for Trump's threats by testing a hydrogen bomb in the Pacific Ocean.