Mr Tillerson has repeatedly called for an open dialogue between the US President and Kim Jong-un after months of furious rhetoric between the two leaders.
But now insiders for the US National Security Council said there will be no talks until Kim ceases his perilous lunge towards becoming a nuclear state.
A spokesman for the Council said: “Given North Korea’s most recent missile test, clearly right now is not the time.”
The statement comes in direct contradiction to Mr Tillerson, who claimed yesterday the US was “ready to talk anytime North Korea would like to talk”.
It follows repeated calls from the US President for his Secretary of State to give up on hopes of an immediate diplomatic solution to rising tensions on the Korean peninsula.
Mr Trump tweeted Mr Tillerson was “wasting his time” in October, claiming the DPRK’s young despot “only understood one thing” in an apparent reference to a military response.
But an anonymous White House official has claimed Mr Tillerson and Mr Trump are in agreement on how to deal with the North Korean tyrant.
The official said: “The administration is united in insisting that any negotiations with North Korea must wait until the regime fundamentally improves its behaviour.
“As the secretary of state himself has said, this must include, but is not limited to, no further nuclear or missile tests.”
While Mr Tillerson claimed on Tuesday it would be “tough to talk” to North Korea if missile tests continued, he did not explicitly state talks would be off the cards if Kim Jong-un launched another missile.
It comes as experts claim the hermit kingdom could launch another deadly missile this Sunday.
Fears the despot could be gearing up for another military provocation have been heightened in recent days after the DPRK’s supreme leader called his top army and government officials to a meeting yesterday.
And an ominous visit to Mount Paektu – often a place used for contemplation by Kim before he launches attacks on his detractors – further raised suspicions of an impending threat.
Now highly regarded North Korean experts at the Center for Strategic and International Studies (CSIS) in Washington DC have warned a test is likely to take place soon.
Analysis carried out by CSIS last month claimed there was an “elevated chance of provocations” in December, while an international expert from the think tank said a “ballistic missile test” was “expected on 17th of December”.
The date coincides with the death of the hermit kingdom’s former autocratic ruler Kim Jong-il – the current ruling Kim’s father.
North Korea has long used anniversaries, including the founding of their military and key dates for the Kim dynasty, as excuses to test fire their potentially deadly weaponry.