President Trump said on Sunday that he told Secretary of State Rex Tillerson Rex Wayne TillersonGary Cohn: 'I haven't made up my mind' on vote for president in November Kushner says 'Alice in Wonderland' describes Trump presidency: Woodward book Conspicuous by their absence from the Republican Convention MORE that it is a waste of time to negotiate with North Korea amid the escalating crisis on the Korean Peninsula.

"I told Rex Tillerson, our wonderful Secretary of State, that he is wasting his time trying to negotiate with Little Rocket Man," the president said.

I told Rex Tillerson, our wonderful Secretary of State, that he is wasting his time trying to negotiate with Little Rocket Man... — Donald J. Trump (@realDonaldTrump) October 1, 2017

"Save your energy Rex, we'll do what has to be done!" he added.

...Save your energy Rex, we'll do what has to be done! — Donald J. Trump (@realDonaldTrump) October 1, 2017

Tillerson said on Saturday that the U.S. was in direct contact with North Korean officials, even though there is no official diplomatic relationship between Washington and Pyongyang.

However, State Department spokeswoman Heather Nauert said North Korea had shown no interest in negotiating on matters related to its nuclear weapons program.

"U.S. diplomats have several open channels in which we can communicate with officials within the North Korean regime," Nauert said Saturday.

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"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 denuclearization," she added.

The war of words escalated between the two countries last month after Trump threatened on the floor of the United Nations to devastate North Korea.

North Korea's foreign minister threatened to test a hydrogen bomb in the Pacific Ocean in response to Trump's address and said the president's tweets about his country amounted to a declaration of war.