Mr Mattis warned that the secretive country’s advancing nuclear and missile programs would undermine, rather than strengthen its security.
He said: “Make no mistake – any attack on the United States, or our allies, will be defeated.
“And any use of nuclear weapons by the North will be met with a massive military response that is both effective and overwhelming.”
The US Defence Secretary said: “I cannot imagine a condition under which the United States can accept North Korea as a nuclear power.”
This comes as he warned that the threat of a nuclear missile attack by North Korea is accelerating.
He warned that the country run by the despot Kim Jong-Un would face a “massive military response” if it used nuclear weapons as he vowed to defeat any attack.
Mr Mattis has made it clear that North Korea is overmatched by the firepower and the bond of the US-South Korea alliance.
In September, North Korea carried out its sixth nuclear test, which was its biggest yet.
It has also carried out a series of missile tests, firing two ballistic missiles over Japan.
Mr Mattis has been in Asia where he has been trying to highlight the importance of diplomacy in solving the crisis.
Mattis’s South Korean counterpart, Defence Minister Song Young-moo, dismissed the idea of deploying tactical nuclear weapons to the peninsula as a response to the North’s advances.
Tensions between the United States and the Korean Peninsula have soared following a series of nuclear and missile tests led by Kim Jong-Un.
Trump – who has threatened to destroy the North if necessary – leaves on his first trip as president to Asia next week, including a stop in South Korea to meet President Moon Jae-in.
Moon, after talks with Mattis on Friday, said the “aggressive deployment” of U.S. strategic assets in the region, which have included overflights by U.S. bombers, had been effective in deterring the North Korean threat.
U.S. intelligence experts say Pyongyang believes it needs the nuclear weapons to ensure its survival and have been skeptical about diplomatic efforts, focusing on sanctions, to get Pyongyang to denuclearise.
Mattis suggested, however, that Pyongyang needed to understand that its weapons programs would not strengthen its defences.
“If it remains on its current path of ballistic missiles and atomic bombs, it will be counter-productive,” Mattis said, adding North Korea would be “reducing its security.”