Mr Mattis is in Seoul for annual defence talks with South Korea.
US President Donald Trump is due to visit South Korea in November as part of a trip to Asia.
In September North Korea carried out its sixth nuclear test, which was its biggest yet.
The bomb was thought to have had a power range from 50 to 120 kilotonnes. A 50kt device would be about three times the size of the bomb that destroyed Hiroshima in 1945.
It has also carried out a series of missile tests, firing two ballistic missiles over Japan in August and September.
South Korea has begun deploying the US Thaad (Terminal High-Altitude Area Defence) missile defence system in response to the threat of a missile attack from the north.
Earlier this month, the US and South Korea also began joint military exercises in waters surrounding the Korean peninsula, involving fighter jets, destroyers and aircraft carriers.
The…
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