His remarks came after a historic summit in Singapore this week between President Donald Trump and North Korean leader Kim Jong Un, where the men signed a joint statement in which Kim committed "to work toward complete denuclearization of the Korean Peninsula."

Quoting Trump at the summit, Mattis said: "The past does not have to define the future."

"But while a possible new avenue to peace now exists with North Korea, we remain vigilant regarding pursuit of nuclear weapons anywhere in anywhere in the world," Mattis said at a US Naval War College graduation ceremony in Rhode Island.

Earlier Friday, Trump told reporters that he has "largely solved" the North Korean nuclear problem.