He added: "Kim Jong-un should take heed of the United Nations Security Council's unified voice. All members unanimously agreed on the threat North Korea poses and remain unanimous in their commitment to the denuclearisation of the Korean Peninsula.
"We are not looking to the total annihilation of a country, namely North Korea, but as I said, we have many options to do so."
Mattis' strong warning comes just hours after North Korea carried out its sixth nuclear test - the most powerful blast to date.
The official Korean Central News Agency (KCNA) said the hydrogen bomb test on Sunday morning, ordered by leader Kim Jong-un, was a "perfect success".
It was Pyongyang's first nuclear test since Donald Trump took office, and marked a direct challenge to the US president, who hours earlier talked by phone with Japanese Prime Minister Shinzo Abe about the "escalating" nuclear crisis in the region.