|Donald Trump says talking to North Korea is a waste of time|
Rex Tillerson, America's top diplomat, disclosed at the weekend the US was in
"direct contact" with Pyongyang over its nuclear and missile programmes.
The State Department said North Korea had shown no interest in dialogue.
"I told Rex Tillerson, our wonderful Secretary of State, that he is wasting his time trying to negotiate with Little Rocket Man," President Trump wrote on Twitter.
"Save your energy Rex, we'll do what has to be done!" he added.
He was speaking in China, where he is hoping to encourage President Xi Jinping to implement recently agreed UN sanctions against North Korea.
Mr Tillerson said North Korea had come up in talks with Xi Jinping
He said: "We have lines of communication with Pyongyang. We're not in a dark situation, a blackout, we have a couple, three channels open to Pyongyang."
The US has not ruled out the use of force to compel Pyongyang to halt missile and nuclear tests, and last week Mr Trump threatened to "totally destroy" the country.
But privately, senior figures admit the military options do not look promising, with South Korea's densely populated capital Seoul in range of the North's artillery.
As Mr Tillerson met China's top diplomats, North Korea's state media produced a new barrage of insults.
A statement branded Mr Trump an "old psychopath" bent on the "suicidal act of inviting a nuclear disaster that will reduce America to a sea of flames".
The US Secretary of State suggested the key to easing diplomatic tensions was putting an end to Mr Kim's missile tests.
He said: "The whole situation is a bit overheated right now. I think everyone would like for it to calm down.
"I think if North Korea would stop firing all the missiles, that would calm down things a lot."