Pressed on whether that might include so-called "kinetic" options that use lethal force, Mattis said: "I don't want to go into that".
Military options available to Trump range from non-lethal actions such as a naval blockade aimed at enforcing sanctions to waging cyber attacks and positioning new US weaponry in South Korea, where the United States has 28,500 troops.
South Korea has raised the possibility of reintroducing nuclear weapons to the peninsula. Mattis acknowledged discussing that with his South Korean counterpart but declined to say whether that option was under consideration.
"We have open dialogue with our allies on any issue that they want to bring up," he said.
US President Donald Trump has hinted that any use of lethal force against North Korea would be overwhelming, using phrases like "fire and fury" that evoke images of nuclear war.
The Pentagon deployed a formation of 14 bombers and fighters over the Korean Peninsula that also included South Korean and Japanese aircraft, the latest show of force in response to North Korea's missile launches and nuclear tests.
The warplanes were dispatched after North Korea launched a ballistic missile over northern Japan last week, triggering a widespread emergency alert for those who call the region home.
Two Air Force B-1B bombers from Andersen Air Force Base in Guam and four Marine Corps F-35B fighters from Iwakuni, Japan, combined with four South Korean F-15K fighters and four F-2 Japanese fighters, US defence officials said.
The aircraft carried out a simulated attack on the Pilsung training range in South Korea, a few dozen kilometres from the demilitarised zone separating the North and South, while using live bombs.
The US and Japanese jets also flew in formation over waters near Kyushu, Japan, a southern portion of the country that is the closest major island to the Korean Peninsula.
The US military released 24 photos of the latest show of force, an apparent message to North Korea and the international community.
- AAP, Washington Post