The new comments, made while Mattis headed for India, followed a shrill war of words between the North Korean and US leaders over Pyongyang's nuclear programme.
Pyongyang's Foreign Minister Ri Yong-Ho said on the sidelines of the UN General Assembly on Saturday that his country could test a nuclear bomb over the Pacific.
"This would be a shocking display of irresponsibility for global health, towards stability, towards non-proliferation," Mattis told reporters on his flight to India.
Trump 'gravest threat to international peace, security': North Korea
He declined to comment when asked if such a test would constitute an act of war.
Amid bitter wrangling between US President Donald Trump and North Korean leader Kim Jong-Un, US bombers and jet fighters flew off the North Korean coast on Saturday in a show of force.
The North's nuclear programme will be one of the regional security topics raised by Mattis with Indian leaders during his three-day stay.
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