North Korea "should cease any consideration of actions that would lead to the end of its regime and the destruction of its people", Mattis said in an August 9 statement.
On Wednesday, Mr. Trump threatened to rain down "fire and fury like the world has never seen" if North Korea did not curb its nuclear programs.
The Kim Jong-Un regime has said it now has the capability of striking the USA mainland after two successful intercontinental ballistic missile (ICBM) tests last month.
Earlier this week, Gen. Kim Rak-Gyom, who heads North Korea's rocket command, said in a statement carried by state media that Pyongyang was "about to take" military action near the US territory of Guam.
Secretary of Defense Jim Mattis said Thursday that the United States military is prepared to respond to an attack from North Korea "should they be needed".
Trump said North Korean leader Kim Jong Un was not going to get away with his "horrific" comments and disrespecting America.
President Donald Trump again stepped up the rhetoric against North Korea on Thursday, saying an earlier threat to unleash "fire and fury" on Pyongyang if it launched an attack was not tough enough.
Meanwhile, France is urging all sides "to act responsibly and to de-escalate" tensions over North Korea's nuclear ambitions.
Britain's UN ambassador said the United Kingdom "stands shoulder to shoulder with the United States" in tackling the nuclear threat from North Korea and making sure it can not pursue its nuclear and ballistic missile programmes.
An attack would require more military assets than the USA now has stationed in the Korean peninsula and east Asia.
The official, who spoke to Newsweek on the condition of anonymity, said war game scenarios conducted by the USA and South Korea indicated that substantial time would be required to move military assets for an attack on the state.
The two discussed responses to North Korean provocations and the security situation on the Korean peninsula, he said. The island has become a talking point in the rhetoric coming from President Trump and North Korea.