DPRK is the acronym of North Korea's official name, the Democratic People's Republic of Korea.
The Pentagon chief's comments came a day after President Donald Trump issued an apocalyptic warning to his North Korean counterpart Kim Jong-Un, telling him Pyongyang faced "fire and fury" over its weapons and ballistic missile programs.
The United States has 28,500 troops in South Korea to guard against the North Korean threat.
The secretary issued a statement in response to news that Pyongyang had successfully developed nuclear warheads small enough to put on the head of a ballistic missile that could reach the U.S.
Mattis added that while the State Department was making diplomatic efforts, the United States and its allies have the most "precise, rehearsed and robust defensive and offensive capabilities on Earth".
Mattis' comments followed North Korea's threats of a missile attack on a USA base on Guam in the Pacific this morning and Donald Trump's unexpected, stark promise to respond with "fire and fury" against the nation last night.
"The (North Korean) regime's actions will continue to be grossly overmatched by ours and would lose any arms race or conflict it initiates".
In September 2016, the regime tested a bomb with a blast estimated at twice the size of the one detonated over Hiroshima, Japan, during World War II. "It is now far stronger and more powerful than ever before", Trump tweeted.
North Korea responded by warning to attack Guam. "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!"
"I think Americans should sleep well at night, have no concerns about this particular rhetoric of the last few days", Tillerson said. The U.N. Security Council unanimously imposed new sanctions on North Korea on Saturday.
While Trump said the nuclear arsenal was more powerful than ever before, US officials say it takes decades to actually modernize nuclear weapons, a move already under way under President Barack Obama's administration, and there are treaties that regulate nuclear expansion.
US Defence Secretary Jim Mattis says they are trying the diplomatic route with North Korea, but also stressed the might of the US would overwhelm the Asian nation's military.
Tens of thousands of United States troops remain stationed in South Korea and in nearby Japan, the only country to have been attacked with nuclear weapons.