Tillerson: Americans should 'sleep well at night' amid N. Korea crisis The secretary of state is pushing for cooler heads and continued diplomacy.

MANILA, Philippines -- While President Trump delivered a brash warning of “fire and fury,” his Secretary of State Rex Tillerson is pushing for cooler heads and continued diplomacy.

The belligerent message from Trump was meant to match the aggressive, at times ridiculous, rhetoric from North Korea, according to Tillerson.

“What the president was doing was sending a strong message to North Korea in a language that Kim Jong Un would understand,” Tillerson told reporters as he traveled back from Southeast Asia. “It was important that he deliver that message to avoid any miscalculation on their part.”

He stopped in the small Pacific island of Guam, a U.S. territory, just hours after North Korea threatened to strike it. But he had no qualms about safety while there, he said. “I do not believe there is any imminent threat, in my own view.”

He later said, “Americans should sleep well at night. I have no concerns about this particular rhetoric over the last few days.”

But back home, there is great concern over the tough talk from Trump.

“North Korea best not make any more threats to the United States,” Trump said Tuesday from his golf course in Bedminster, New Jersey. “They will be met with fire, fury and, frankly, power, the likes of which this world has never seen before.”

Intentionally or not, those remarks escalated the back-and-forth between the U.S. and North Korea, hours after reports emerged that North Korea may have developed the technology to miniaturize a nuclear warhead and fit it onto a ballistic missile.

The newly public report from U.S. intelligence agencies seemed to spur Trump, but Tillerson called for full steam ahead on his policy of “peaceful pressure,” after a series of meetings at the Association of Southeast Asian Nations summit in Manila, the Philippines.

“We do not seek to be a threat to them, but we have to respond to the serious threats that they make towards us,” Tillerson said.

Despite Trump’s apocalyptic language, Tillerson said the U.S. wasn't closer to military action and that Kim still has a “way out” through “talks, with the right expectation of what those talks will be about” — an end to his violent regime’s nuclear and ballistic missile programs.

“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,” he added.

At the ASEAN gathering, Tillerson said the U.S. had success in pushing for increased isolation of North Korea, including full implementation of new United Nations sanctions.

In a win for him and Nikki Haley, the U.S. ambassador to the U.N., the Security Council voted Saturday to add sanctions against North Korea, targeting its export revenue sources.

ABC News’ Luis Martinez contributed to this report.