The secretary called on North Korea to "stop isolating itself and stand down its pursuit of nuclear weapons".
Mattis' statements on Wednesday added to the increasingly heated rhetoric between North Korea and the United States. While our State Department is making every effort to resolve this global threat through diplomatic means, it must be noted that the combined allied militaries now posses the most precise, rehearsed, and robust defensive and offensive capabilities on Earth.
The country also, according to another intelligence assessment, is estimated to have at least 60 nuclear weapons.
Mattis has previously testified before the House Appropriations Committee that a fight with North Korea would be "more serious in terms of human suffering" than anything since the original Korean War ended in 1953.
"My first order as President was to renovate and modernize our nuclear arsenal".
His comments punctuate President Donald Trump's warning that North Korea will be met with "fire and fury" if it threatens the US. "Hopefully we will never have to use this power, but there will never be a time that we are not the most powerful nation in the world!"
Mattis' words are a steadfast declaration of the overwhelming military might of the United States and its allies, though he does offer a few more nods towards diplomacy as a solution to what increasingly looks like a bona fide geopolitical crisis.
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And Secretary of State Rex Tillerson has made clear he is open to negotiations if Pyongyang freezes its nuclear and missile programs.
Guam hosts strategic U.S. military installations - including both a naval and an air force base - and is more than 3,400km from North Korea.
With his "fire and fury" warning, Trump was "sending a strong message to North Korea in language that (North Korean leader) Kim Jong Un would understand, because he doesn't seem to understand diplomatic language", Tillerson said. "As said, they will be met with fire, fury, and, frankly, power the likes of which this world has never seen before", he said.
North Korea's actions drew a punishing response from several of the world's major countries. The aircraft flew over Japanese airspace before passing over the Korean Peninsula.
The Washington Post reported on Tuesday that North Korea had obtained the capability of creating a nuclear warhead small enough to place on a missile.
Tens of thousands of USA troops remain stationed in South Korea and in nearby Japan, the only country to have been attacked with nuclear weapons.