Mr Tillerson said "lines of communications" were being used and the U.S. was "probing" the possibility of more formal talks with Pyongyang, adding: "Stay tuned".
North Korea is working on a nuclear-tipped missile able to reach the United States mainland, and it will make thousands of refugees move to China, NBC News reported.
But the State Department later said that North Korea had shown no interest in such discussions and Trump wrote that he regarded any possible talks as futile.
Trump tweets this advice to Secretary of State Rex Tillerson: "Save your energy, Rex, we'll do what has to be done!"
"I think if North Korea would stop firing all the missiles, that would calm down things a lot". "We have a couple. three channels open to Pyongyang".
Fears of a conflict in the region reached boiling point recently after President Trump warned he would "totally destroy" Kim's regime.
So far, Rex Tillerson, has ensured that the China -main economic partner of North Korea - was not an intermediary in the communications between Washington and Pyongyang: what are "our own channel",-he said.
The November meeting of the two leaders will be grander and more choreographed than the informal talks in Florida that were most memorable for Trump's ordering a missile strike on Syria and then informing Xi about it afterward as they ate chocolate cake.
But with his words the secretary of State was effectively confirming an August story from the Associated Press that claimed the Trump administration was "quietly engaged in back channel diplomacy with North Korea for several months".
The standoff has entered a new, more risky phase since then as Kim and Trump have exchanged personal insults and threats of war. "They're a little overheated right now and I think we need to calm them down first".
As Tillerson stated, the USA and the DPRK governments communicate directly over the issue of "nuclear and missile tests".
Other than North Korea, the US and China have other security concerns to address.
North Korea has ramped up its testing of nuclear weapons and long-range missiles as the United States has pushed forward on global economic sanctions against the reclusive nation.
Tillerson, facing criticism at home for his muted impact as the top US diplomat, may also be seeking to put his own stamp on the relationship.
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