But "the question that now needs to be answered is whether North Korea's missile program has progressed to the level of being such an inherent threat that the Pentagon would recommend targeting a missile even if its trajectory did not indicate it would hit the US or its allies", CNN quoted a senior USA official as implying.
North Korea has said the tests are meant to develop the capability to hit USA territory with a nuclear weapon.
The news network reported its information comes from an unnamed official who it said to be familiar with options being discussed by the Trump administration.
"Yes, I don't want to go into that", Mattis said, agreeing that his closely-held military option involved kinetic action, a euphemism to describe lethal military force.
The US jets flew alongside four South Korean F-15K jet fighters as part of "routine" training, the statement said, adding that the allies would continue such exercises to "improve their joint operation capabilities against contingencies".
Mattis noted that there are military options that would not put South Korea at grave risk, but declined to explain further. "Are we talking kinetic options as well?" a reporter asked in a follow-up.
Previously, Mattis said a war with North Korea would "involve the massive shelling of an ally's capital, which is one of the most densely packed cities on earth", in reference to Seoul.
South Korea and the United States, and separately Russian Federation together with China, started military drills on Monday, in a show of force against North Korea.
Chinese President Xi Jinping and U.S. President Donald Trump spoke by telephone about keeping pressure on North Korea using economic sanctions imposed through the United Nations, the White House has said.
The US aircraft flew close to the North Korean border before returning to their base in Guam.
North Korea has fired two missiles over US ally Japan recently, on August 29 and September 15.
Last week, North Korea launched an intermediate-range ballistic missile that travelled 2,300 miles and passed over the Japanese island of Hokkaido before landing in the northern Pacific.
In his remarks today, Mr Mattis made clear that the United States and Japan were prepared for future missile threats.
It was the country's longest-ever test flight of a ballistic missile.