China and Russia responded positively to Tillerson's remarks, even after the White House appeared to put his proposal in question by saying that US President Donald Trump's "views on North Korea have not changed."
While White House press secretary Sarah Sanders did not spell out the president's views, Trump in the past has chided his secretary of state for "wasting his time" trying to negotiate with Pyongyang.
In Beijing, foreign ministry spokesman Lu Kang said China took note of Tillerson's remarks and expressed hope that the United States and North Korea take "meaningful steps towards dialogue and contact."
"We welcome all efforts that are conducive to easing tension and resolving differences through dialogue," Lu said.
In Moscow, Kremlin spokesman Dmitry Peskov told journalists: "We can state that such constructive statements impress us far more than the confrontational rhetoric that we have heard up to now. Undoubtedly this can be welcomed."
Even as Tillerson stressed the importance of a negotiated end to the standoff, North Korean leader Kim Jong-Un vowed to make his nation "the strongest nuclear power and military power in the world."
Trump has promised that Kim will not be allowed to complete his effort to develop nuclear-armed intercontinental ballistic missiles capable of reaching mainland US cities.
To this end, Tillerson has overseen a global diplomatic effort to isolate Pyongyang and stifle its economy through UN sanctions and, ultimately, the threat of US military force.
In two public appearances Tuesday, he warned that these efforts would continue until "the first bomb drops" and that Washington "simply cannot accept a nuclear-armed North Korea."
But he said the door to talks with Kim's regime was open, and left the opening wider than he had before, backing away from his former insistence that Pyongyang accept in principle to disarm.
"We're ready to have the first meeting without preconditions," Tillerson told a meeting of the Atlantic Council policy forum, speaking of the possibility of laying out a roadmap of goals.
"It's not realistic to say we're only going to talk if you come to the table ready to give up your program. They have too much invested in it."
A senior UN official returning from Pyongyang said that North Korean officials had told him it was important to prevent war but offered no concrete proposal for talks.
"They agreed that it was important to prevent war," Jeffrey Feltman, the UN's political affairs chief, told reporters after briefing the Security Council on his trip.
Feltman met with North Korea's Foreign Minister Ri Yong-Ho and Vice Foreign Minister Pak Myong-Kuk during his visit to Pyongyang over the weekend -- the first by a high-ranking UN official since 2011.
Devastating conflict
Some in Washington see Tillerson's latest rhetoric as a climbdown.
Sanctions expert Anthony Ruggiero, of the hawkish Foundation for Defense of Democracies, said talks should not begin until the US has a way to verify nuclear testing is not continuing.
Earlier, in an end-of-year speech to State Department staff and US diplomats, Tillerson stressed the importance of the sanctions regime in forcing North Korea to the table.
Despite hopes that China will do more to cut off oil supplies, international action has forced North Korea's fuel prices up by around a half and cost it $2.3 billion in lost exports, he said.
And Tillerson added that he would see it as a personal failure if his efforts came up short and US Defense Secretary Jim Mattis is forced to take military action to deny the North its arsenal.
But even if Tillerson remains "confident" that the US strategy is paying off, there was little sign of this in Pyongyang, where Kim gave a typically bellicose speech to workers.
According to North Korea's state news agency KCNA, Kim said his country "will victoriously advance and leap as the strongest nuclear power and military power in the world."
His latest boast came after the November 29 launch of the Hwasong-15 ICBM, a missile which the North claimed could deliver a "super-large heavy warhead" anywhere on the US mainland.
Invective
Outside experts agree the rocket appears to have the range, but some are skeptical that Pyongyang has the technology to allow the rocket to survive re-entry to the Earth's atmosphere.
But US officials have been warning privately for months that Pyongyang is on the verge of a breakthrough, and Tillerson's public confidence appears aimed at much at Trump as at Kim.
Both the US and North Korean leaders have a penchant for warlike rhetoric and personal invective that risks plunging east Asia into a devastating conflict that could leave millions dead.
Trump habitually refers to Kim as "Little Rocket Man" and has threatened to utterly destroy his regime with "fire and fury." North Korea has branded Trump a mentally disturbed "dotard."
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