Mattis said, noting the USA has "many military options".
Mattis spoke at the White House after meeting with Trump, Vice President Mike Pence and other members of Trump's national security team.
Although analysts said they could not verify the claim, they added that the force of the blast suggested North Korea had developed a weapon equivalent to 120 kilotons - an order of magnitude more powerful than the bomb dropped on Nagasaki.
Following Trump's Twitter scolding of South Korea, a longtime US ally, Mattis said after the White House meeting that "the commitments among the allies are ironclad", referencing Japan, South Korea and the United States.
Mattis' statement does not say the USA would not strike first - it actually suggests America's military might, because it uses the word "threat" as opposed to action or attack.
On Sept. 3, North Korean media announced that the Kim regime had successfully tested a hydrogen bomb in an underground test site.
Mnuchin would not rule out the possibility of Trump launching military action, and said Trump will "consider everything". The warning arrived after the Kim Jong-un regime reportedly tested a hydrogen bomb.
His comments are coming after leaders around the world jointly condemned North Korea's testing of its sixth nuclear missile.
"We are going to work with our allies, we'll work with China, but people need to cut off North Korea economically".
"The two leaders agreed to stick to the goal of denuclearisation on the Korean Peninsula and keep close communication and coordination to deal with the new situation", Xinhua said in a brief dispatch.
North Korea's traditional ally China also denounced the test, slamming Pyongyang for ignoring global condemnation of its atomic weapons program. "North Korea is a rogue nation which has become a great threat and embarrassment to China, which is trying to help but with little success".
Following the meeting with military officials, the President said "we'll see" when asked if Washington was considering military action in response to the North's sixth nuclear test.
Boris Johnson, the British Foreign Secretary, said North Korea had the power to "vaporise" large parts of the population of South Korea even without nuclear weapons. The UN Security Council unanimously voted last month to impose sanctions on Pyongyang after the country launched a series of ICBMs.
Mattis also added that; "Kim Jong-un should take heed of the United Nations Security Council's unified voice".
Abe also telephoned with Trump to discuss the test, according to a White House statement issued late on Sunday.
North Korea's state-run television broadcast a special bulletin Sunday afternoon to announce the test.