A new report says Pyongyang's nuclear programme is progressing.
"The rhetoric is up to the president", Mattis said.
Speaking at an event in California, Mattis said his mission and responsibility was to have military options ready "should they be needed" but stressed the USA effort is now focused on diplomacy.
President Trump, however, drew criticism earlier this week when he threatened North Korea with "fire and fury."Mattis told reporters on the flight Wednesday the president has the prerogative to use whatever rhetoric he chooses".
The Pentagon chief on Wednesday issued a carefully worded statement telling North Korea it would be "grossly" outmatched in any conflict with the USA, and warning Pyongyang to stop considering any action that risked "the destruction of its people".
"The tragedy of war is well enough known". Striking a defiant tone on Thursday evening, he told reporters: "Maybe it wasn't tough enough". "But the last person in the world you want to give a missile with a nuclear weapon on top is Kim Jong Un, given the way he's treated his own people, and what he's said about us". "And I don't think we are".
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But UN Secretary General António Guterres hinted that Trump's remarks risked derailing the diplomatic process.
"That would be the clearest indication that we were headed toward war", Pollack says. "That shows where the Trump administration goes in terms of the prioritizing of the threat but also how to deal with it in a diplomatically effective manner".
Diplomats from each country, including USA envoy to North Korea Joseph Yun and North Korean diplomat Pak Song Il are maintaining a relationship with each other in NY, fostered as well by outside groups that favor direct engagement.
The issue came to the fore again this week when US intelligence analysts assessed that North Korea had produced a miniaturized nuclear warhead, according to multiple sources, which would bring the country a significant step closer to being able to fire a nuclear-tipped warhead at the USA or its allies.
There are about 29,000 American troops permanently stationed in South Korea.