Washington (CNN) President Donald Trump's blunt threat to North Korea that it could face the United States' "fire and fury" could undermine work the rest of his Cabinet has been doing to defuse growing tensions in Asia.

For weeks, Secretary of State Rex Tillerson has been building what he calls a "peaceful pressure" campaign, roping international partners into a broad effort to push the Democratic People's Republic of Korea to stop brandishing its missiles and weapons and come to the negotiating table.

The top US diplomat has paired that endeavor with an equally important but more subtle project: sending messages of reassurance to China and other Asian nations that the US' aim isn't to destroy North Korea and upend the region, but simply to engage Pyongyang in talks.

Tillerson delivered that message most explicitly August 1 before setting out on a trip to Asia that has taken him to Manila, Malaysia and Thailand this week.

"We do not seek a regime change," Tillerson told reporters before his departure. "We do not seek the collapse of the regime, we do not seek an accelerated reunification of the peninsula, we do not seek an excuse to send our military north of the 38th parallel."

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That messaging is key for countries across Asia that have trade and other ties to North Korea, but it's especially crucial for China, which has outsized influence because it accounts for 90% of the DPRK's trade. Beijing's national security interests are at stake if the nation of about 25 million people collapses.

That would send millions of refugees pouring over the border into China, burdening its cities and resources. From a longer term strategic view, Chinese leaders fear the prospect of a unified Korean peninsula that would put US forces -- 28,000 of which are now in South Korea -- right on their doorstep.

Beyond speaking directly to North Korea, Tillerson's message "is certainly meant for China," said Victor Cha, a senior fellow at the Center for Strategic and International Studies. And he adds that Tillerson was trying to reach other audiences as well.

His reassurance is also meant for Asian countries, "all of whom have some form of relationship with North Korea to show them the United States is not about North Korea's collapse," Cha said.

Diplomatic signals

And there's an even wider circle for Tillerson's diplomatic signals.

"More broadly, it's for the international community, to have them understand that when we call for sanctions and when we're pressing for sanctions, the purpose is not to try to collapse North Korea, but to compel them to come back to the negotiating table," Cha said.

That's a particularly important message for countries like Russia, which wields a crucial Security Council vote and where there are deep suspicions about the US penchant for "regime change."

As China and other Asian nations balance the threat posed by North Korean leader Kim Jong Un against their desire for stability, Tillerson's challenge has been to bring them along. It remains to be seen how Trump's fiery threats will affect US allies or the regional dynamic.

For now, it's not getting any calmer. North Korea's military is "examining the operational plan" to strike areas around Guam with medium-to-long-range strategic ballistic missiles, the state run KCNA said Wednesday. The statement, from a spokesman from the Strategic Force of the Korean People's Army, warned that recent US military maneuvers -- a reference to the flight of two US B1B bombers over the Korean peninsula Monday -- "may provoke a dangerous conflict."

Pyongyang has steadily increased its testing, launching its fifth nuclear test in September and ratcheting up missile tests exponentially.

US intelligence analysts have assessed, but not concluded, that North Korea has produced a miniaturized nuclear warhead, according to multiple sources familiar with the analysis of North Korea's missile and nuclear program.

Pyongyang launched its second ICBM in late July in a test that demonstrated the potential to reach the US. It was the 11th missile test that North Korea has conducted in 2017. Cha notes that if the rate of tests is extrapolated over the rest of Trump's term, Pyongyang would fire off nearly 100 tests.

That compares to 64 missile tests over the eight years of President Barack Obama's time in the White House. And it marks a stark acceleration from 1994 to 2008, when North Korea did a total of 16 missile tests, Cha said.

'We are not your enemy'

It's that level of intensification that led Tillerson on August 1 to say that, "we're trying to convey to the North Koreans we are not your enemy, we are not your threat, but you are presenting an unacceptable threat to us, and we have to respond."

US officials had recently begun to say they see Tillerson's efforts bearing fruit. They point to the 15-0 Security Council vote on August 5 to impose new sanctions on North Korea, which both China and Russia backed.

China's attitude toward North Korea appears to be shifting, they say, albeit very slowly, comparing Beijing to a slow-turning ship. The US believes Pyongyang's second launch of an intercontinental ballistic missile, and South Korea's decision to go ahead with anti-aircraft defenses, are influencing China's thinking.

Indeed, some officials say that steps the US is taking to bolster military defenses in South Korea, and Seoul's more hawkish response to the launches, is creating another kind of strategic pressure on China.

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If North Korea continues its aggressive pursuit of nuclear weapons and the means to deliver them, other nations like Japan, South Korea and even Vietnam could pursue nuclear weapons or increase regional demand for anti-ballistic missile defense systems.

That would alter the regional balance of power and potentially hurt regional economic growth -- which is crucial for China's economic and political stability.

Chinese Foreign Minister Wang Yi said that his country would pay the largest price for the new UN sanctions against North Korea because of its "traditional economic ties" to Pyongyang -- but that it's a necessary step.

"Given China's traditional economic ties with North Korea, China more than anyone will pay a price for implementing the resolution," Wang said Monday a regional security forum in Manila.

"However, in order to maintain the international nuclear non-proliferation system and regional peace and stability, China will, as always, enforce the full content of relevant resolutions in a comprehensive and strict manner," Wang said, according to a statement from the foreign ministry Tuesday.