President Donald Trump tweeted about "Little Rocket Man" again on Sunday.
His comments come a day after Mr Tillerson revealed that U.S. officials had some communication channels open with Pyongyang, despite the escalating war of words between the leaders of both countries.
Asked how he could know whether the North would even contemplate coming to the table to negotiate away its growing nuclear arsenal, Tillerson told reporters in Beijing: "We are probing, so stay tuned".
The disclosure that the USA had direct channels to North Korea underscored Mr Tillerson's role as a moderate within the administration.
Chinese and U.S. teams should implement consensus reached by the two heads of state, grasp the direction of bilateral relationship, respect each other, and focus on cooperation while dealing with differences properly, Xi said. "Directly, through our own channels".
"Save your energy Rex, we'll do what has to be done!"
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However, Chelsea will surely miss Morata more than City will Sergio Aguero and United will Pogba. His first start of the season went amazingly well and he was Chelsea's best player on the pitch.
Early last month, North Korea tested what it claims to have been a hydrogen bomb underground - it's sixth nuclear test and first since Trump took office.
He said in Beijing: "I think the whole situation is a bit overheated right now".
Some commentators seized on Trump's tweets as evidence that he was either undermining Tillerson personally or his diplomacy, or both.
"Rocket man is on a suicide mission for himself and for his regime", Trump said in his address to the U.N. General Assembly.
Asked if the President's tweets indicate he has chose to abandon the diplomatic track on North Korea, a senior administration official told CNN: "We are still committed to a diplomatic approach". At the same time, increased sanctions and diplomatic pressure have done little to force North Korea to alter course.
But nearly as soon as Tillerson's trip was over, President Donald Trump swiftly undermined his secretary of state's outreach.
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"Obviously it would help if North Korea would stop firing off missiles".
In early August, Trump warned the U.S. would rain down "fire and fury" on North Korea, saying the United States would destroy the nation of some 25 million people if its dictator's threats against the USA and its allies continued. "That would calm things down a lot".
China argues that sanctions alone can not solve the impasse, and has urged Washington to cool its rhetoric and open a dialogue with North Korea.
Kim responded by saying he would "surely and definitely tame the mentally deranged us dotard with fire".
Not long afterward, North Korea's foreign minister said Trump's comments - and one tweet in particular, saying Pyongyang might not "be around much longer!" - were tantamount to a "clear declaration of war".
Trump has vacillated between direct personal attacks on the North Korean leader and a willingness to negotiate. Trump's planned visit next month will come weeks after Xi is expected to receive a new five-year term as leader of the ruling Communist Party.
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