The US naval move will certainly raise tensions in the region and comes hard on the heels of a US cruise missile strike on Syria that was widely interpreted as putting Pyongyang on warning over its refusal to abandon its nuclear ambitions.
North Korea denounced Thursday's attack as an act of "intolerable aggression" and one that justified "a million times over" the North's push toward a credible nuclear deterrent.
"That is not our objective and so the whole reasons underlying the development of a nuclear program in North Korea are simply not credible," Tillerson told the ABC programme "This Week."
He said the United States expects China, the main ally of North Korea, to do more to rein in the regime in Pyongyang.
"They have indicated that they will and I think we need to allow them time to take actions," Tillerson said.
"Presidents before and President Trump agreed that that is unacceptable, that what must happen is the denuclearization of the peninsula," McMaster told Fox News.
"The president has asked them to be prepared to give us a full range of options to remove that threat," he added, apparently referring to Trump's advisers.
Pyongyang is on a quest to develop a long-range missile capable of hitting the US mainland with a nuclear warhead, and has so far staged five nuclear tests, two of them last year.
North Korea on Wednesday fired a medium-range ballistic missile into the Sea of Japan ahead of a US-China summit.
The isolated North is barred under UN resolutions from any use of ballistic missile technology.
In February, the North simultaneously fired four ballistic missiles off its east coast, three of which fell provocatively close to Japan, in what it said was a drill for an attack on US bases in the neighboring Asian country.
A nuclear-capable SLBM system would take the North's threat to a new level, allowing deployment far beyond the Korean peninsula and a "second-strike" capability in the event of an attack on its army bases.
Asked if development of a long range ballistic missile would mark 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."
Trump has threatened unilateral action against the reclusive communist state, a threat that appeared more palpable after Thursday's strike on a Syrian airfield following an apparent chemical attack.
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