"My responsibility is to have military options if needed", Mattis told a group of reporters in Mountain View, California, where he was visiting a new Department of Defense arm created to speed the integration of new technologies into the US military.
On Thursday, Mr. Mattis declined to comment whether he was taken aback by Mr. Trump's harsh rhetoric.
Tension in the region has risen since the reclusive North, which staged two nuclear bomb tests previous year and launched two intercontinental ballistic missile tests in July in defiance of world powers.
Defense Secretary Jim Mattis said that the North Korean regime should cease any consideration of actions that would "lead to the end of its regime and the destruction of its people".
The Pentagon has prepared a plan involving a B-1B heavy bomber attack against the Democratic Peoples Republic of Korea which is ready should President Trump, as Commander in Chief of the U.S. Armed Forces, decide to order an attack, NBC News reported.
Secretary of State Rex Tillerson told reporters on Wednesday that Americans had "nothing to fear" from Trump's remarks, and that they had instead been an attempt to use language that Kim Jong Un "would understand".
A new report says Pyongyang's nuclear programme is progressing.
Mattis said that the USA effort to counter the nuclear missile ambitions of North Korean leader Kim Jong Un is being "diplomatically led".
"The best way to show how (the threat) is widely gauged, is to look at last weekend when the UN Security Council voted unanimously to characterize this as a North Korean threat to the world's community", he said.
An attack would require more military assets than the US now has stationed in the Korean peninsula and east Asia. We call on the relevant parties to be cautious with their words and actions, and contribute more toward easing tensions and enhancing mutual trust, ' Geng said in a statement.
The former four-star general declined to provide any additional insight to a statement released Wednesday, warning that the North's continued provocations - including alleged plans for an attack against USA forces in Guam by Pyongyang - "would lead to the end of its regime and the destruction of its people". "He would lash out militarily, at a minimum against South Korea", Admiral Stavridis said to NBC.
The two discussed responses to North Korean provocations and the security situation on the Korean peninsula, he said.