Mr Tillerson broached the possibility of dialogue with the secretive communist state out of a desire to “just meet”.
He added that such talks would need to occur amid a “period of quiet” from North Korea, his suggestion still extended a diplomatic opening to a nation that has shown few signs of restraint.
However, other Trump administration officials said no negotiations could begin until North Korea renounced its belligerent posture.
The pariah state has conducted multiple ballistic missile tests in recent months, boasting after its last one that it could strike the mainland United States, and threatened American allies with annihilation.
“Clearly right now is not the time,” an unnamed National Security Council official told Reuters.
Responding to a question about whether Mr Tillerson’s position differed from the White House’s policy, State Department spokeswoman Heather Nauert said “the Secretary was not creating any new policy” and that he was “on the same page as the White House.
“Our policy remains exactly the same as it was,” Ms Nauert said, calling diplomacy the administration’s “top priority” and saying “we remain open to dialogue when North Korea is willing to conduct a credible dialogue on the peaceful de-nuclearisation of the Korean peninsula. We are not seeing any evidence that they are ready to sit down and have those kinds of conversations”.
“When somebody is shooting off ballistic missiles, when someone is conducting advanced nuclear tests, they’re not showing any kind of interest or seriousness about wanting to sit down too talk,” she added.
Mr Tillerson has diverged from other administration officials in the past. He was said to support keeping America in the Paris climate pact, cutting against Donald Trump’s decision to pull the country from the agreement.
There have been rumours in recent weeks that the White House has batted down rumours that Mr Trump was seeking to replace Mr Tillerson.
While the President has urged a peaceful solution to escalating tensions on the Korean peninsula, he has also provoked the country’s leadership by nicknaming leader Kim Jong-un “Little Rocket Man”.
In a United Nations speech, he also warned that America would “totally destroy” North Korea if necessary — a statement that Pyongyang called a “declaration of war”.