His comments come after the North Korean military threatened a missile strike near the U.S. territory of Guam, in response to comments made by President Donald Trump and a Pentagon bomber operation in the region.
Mattis said North Korean leader Kim Jong Un should "take heed" of the U.N. Security Council's statement that Pyongyang poses a global security threat.
"The [Democratic People's Republic of Korea] must choose to stop isolating itself and stand down its pursuit of nuclear weapons," he said, using the name North Korea calls itself. "The DPRK should cease any consideration of actions that would lead to the end of its regime and the destruction of its people."
On Tuesday, Trump warned North Korea not to make any more threats against the United States. In July, North Korea said it would "strike a merciless blow" at the United States if Washington ever attempted to remove Kim from power.
"They will be met with fire and fury like the world has never seen," Trump said from his golf club in Bedminster, N.J. "[Kim] has been very threatening beyond a normal state and as I said they will be met with fire and fury and frankly power the likes of which this world has never seen before."
Earlier Wednesday, U.S. Secretary of State Rex Tillerson defended Trump's remarks.
During a brief scheduled stop in Guam, Tillerson suggested Trump's rhetoric is a strategy he is using as head of state to communicate clearly with Kim.
"What the president is doing is sending a strong message to North Korea in language that Kim Jong Un would 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 that the U.S. has the unquestionable ability to defend itself, will defend itself and its allies, and I think it was important that he deliver that message to avoid any miscalculation on their part."
Mattis said that though the State Department is making efforts to resolve the threat using diplomatic means, allied militaries possess "robust defensive and offensive capabilities."
"The DPRK regime's actions will continue to be grossly overmatched by ours and would lose any arms race or conflict it initiates," he said.
Later Wednesday morning, Trump tweeted about the United States' nuclear capabilities amid tensions with the nuclear-capable North Korean regime. He said the U.S. nuclear arsenal is the most powerful it's ever been under his leadership.
"My first order as president was to renovate and modernize our nuclear arsenal. It is now far stronger and more powerful than ever before," Trump wrote. "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!"
Guam is home to Anderson Air Force Base, from which two U.S. B-1B bombers deployed on a mission with the South Korean and Japanese air forces on Monday. The aircraft flew over Japanese airspace before passing over the Korean Peninsula.
"I think what the president was just reaffirming is that the United States has the capability to fully defend itself from any attack, and our allies, and we will do so," Tillerson said. "So the American people should sleep well at night."