WASHINGTON -- Secretary of State Rex Tillerson urged calm and said Americans should have "no concerns" after North Korea and President Donald Trump traded fiery threats, insisting Wednesday he doesn't believe there is "any imminent threat."

"Americans should sleep well at night," Tillerson said.

In more tranquil terms, Tillerson sought to explain the thinking behind Mr. Trump's warning to Pyongyang that it would be "met with fire and fury like the world has never seen" if it made more threats to the United States. Tillerson said Mr. Trump was trying to send a strong and clear message to North Korea's leader so that there wouldn't be "any miscalculation."

"What the president is doing is sending a strong message to North Korea in language that Kim Jong Un can understand, because he doesn't seem to understand diplomatic language," Tillerson said. "I think the president just wanted to be clear to the North Korean regime on the U.S. unquestionable ability to defend itself, will defend itself and its allies."

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He said North Korea's escalating threats showed it was feeling the pressure from a successful U.S. strategy.

Tillerson downplayed any speculation that the alarming developments suggested the U.S. was moving closer to a military option to dealing with the crisis over the North's nuclear and ballistic missile programs.

"Nothing that I have seen and nothing that I know of would indicate that the situation has dramatically changed in the last 24 hours," Tillerson said.

Nonetheless, as CBS News correspondent Ben Tracy reports, the Chinese government fears the escalating war of words between Pyongyang and Washington will spark a regional arms race -- which already seems to be happening.

South Korean President Moon Jae-In is calling for a complete overhaul of South Korea's military in the face of North Korea's rapidly evolving nuclear capabilities, and in Japan, some lawmakers are pushing for new weapons that could give the country a preemptive strike capability, reports Tracy.

In response to a query from CBS News, the Chinese government would only say that, "the situation on the Korean peninsula is highly sensitive. We hope the parties will be cautious with words and behavior and stop provoking each other and avoid escalation."

Tillerson spoke to reporters aboard his plane as he returned from Malaysia to Washington, stopping along the way in Guam. Hours earlier, North Korea's army had said in a statement it was exploring plans for attacking the tiny U.S. territory, which houses U.S. military bases and is a common refueling stop for U.S. government aircraft traversing the Pacific Ocean.

Tillerson said he never considered re-routing his trip from Malaysia so as to avoid stopping in Guam. Though he insisted there was no imminent threat, he noted that even if there were, "the North Korean missile capability can point in many directions, so Guam is not the only place that would be under threat."

The comments put Tillerson once again in the role of translating the president's aggressive rhetoric into more diplomatic terms, and of working to minimize the chances of a public panic. Though it's extremely unlikely the North would risk annihilation by pre-emptively attacking American citizens, the escalating rhetoric has heightened concern that a miscalculation could spiral out of control and lead to military conflict - a concern that residents of Guam said they felt particularly acutely.

Tillerson, who spent the past days in Asia working the North Korea conflict, said he didn't believe a new diplomatic strategy was needed. To the contrary, he said the latest threat from the North suggested the current strategy was working. After months of frustration over China's reluctance to pressure Pyongyang economically, the U.S. on Saturday secured a unanimous U.N. Security Council vote to authorize sweeping new sanctions that target one-third of the North's exports.

"The pressure is starting to show," Tillerson said. "I think that's why the rhetoric coming out of Pyongyang is beginning to become louder and more threatening. Whether we've got them backed into a corner or not is difficult to say, but diplomatically, you never like to have someone in a corner without a way for them to get out."

To that end, Tillerson said there was still an off-ramp available to Pyongyang: A return to negotiations with the U.S., a step that Tillerson has previously said can happen only if Kim Jong Un's government gives up its nuclear aspirations, starting with an extended pause in missile tests.

"Talks," Tillerson said when asked if North Korea had a way out. "Talks, with the right expectation of what those talks will be about."