DPRK is the acronym of North Korea's official name, the Democratic People's Republic of Korea. "The DPRK should cease any consideration of actions that would lead to the end of its regime and the destruction of its people", Mattis said.
A day earlier Trump warned the North against threatening the US.
It comes following an exchange of threats and boasts of nuclear power by President Donald Trump and North Korea. They evoked President Harry Truman's announcement of the U.S. atomic bomb dropped on Hiroshima, Japan, in 1945, in which he warned of "a rain of ruin from the air, the like of which has never been seen on this earth".
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.
Mattis' statement appears to reference Tuesday night's release from the North Korean army, which said it was considering striking Guam with nuclear-capable Hwasong-12 intermediate-range missiles.
Mattis told North Korea that its actions "will continue to be grossly overmatched by ours", and that Pyongyang would lose any arms race or conflict that it starts with the US.
The North Korean regime has conducted 12 tests so far this year, with one ICBM test conducted in late July sending a missile 2,300 miles into space and 45 minutes into the air.
North Korea's actions drew a punishing response from several of the world's major countries.
Trump followed his threat with a tweet Wednesday declaring the U.S.is more than ready for a war.
He was responding to reporters' questions on the North Korean nuclear capabilities.
Mattis has warned that North Korea now poses the most urgent threat to USA peace and security, but also that any war with Pyongyang would include "probably the worst kind of fighting in most people's lifetime", citing the threat posed by hundreds of North Korean rocket launchers and artillery pieces aimed at Seoul. The U.N. Security Council unanimously imposed new sanctions on North Korea on Saturday.
Robert Kelly, professor of political science at Pusan National University, told Al Jazeera that both North Korea and Trump were nearly certainly exaggerating in their respective rhetoric, as a conflict would be disastrous - and that Trump was likely stepping up the rhetoric to pressure China into taking action to curb North Korea's behaviour.