"If you violate international agreements, if you fail to live up to commitments, if you become a threat to others, at some point a response is likely to be undertaken," Tillerson told ABC's 'This Week'.
There was little doubt the missile strikes would be seen in Pyongyang as a message. The North has long claimed that the US is preparing some kind of assault against it and justifies its nuclear weapons as defensive in nature.
President Donald Trump's national security adviser, HR McMaster, described the decision to send the carrier group as "prudent". He said Trump and Chinese president Xi Jinping had agreed that North Korea's pattern of "provocative behaviour" was unacceptable and the US was acting accordingly.
"This is a rogue regime that is now a nuclear-capable regime...So the president has asked us to be prepared to give him a full range of options to remove that threat to the American people and our allies and partners in that region," McMaster said on 'Fox News Sunday'.
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The comments were made by a Foreign Ministry official and carried by North Korea's state-run Korean Central News Agency today. The report did not name the official, which is common in KCNA reports.
In appearances on the Sunday news shows, Tillerson said advances in North Korea's ballistic missile programme concerned the US the most. Asked on ABC if development of an intercontinental missile was a "red line" for Trump, Tillerson said: "If we judge that they have perfected that type of delivery system, then that becomes a very serious stage of their further development."