The missile launches coincided with Trump's first official encounter with Chinese President Xi Jinping in Florida to discuss North Korea, among other things.
The U.S. launched 59 Tomahawk missiles Thursday night against the Syrian air base where Bashar Assad's government had days earlier fired off a devastating chemical weapon attack that left more than 85 people in the town of Khan Sheikhoun dead.
However Tillerson added that the objective is a denuclearized Korean Peninsula and that Washington has "no objective to change the regime in North Korea".
"Presidents before and President Trump agreed that that is unacceptable, that what must happen is the denuclearisation of the peninsula", US National Security Adviser H.R. McMaster told Fox News on Sunday.
A day before the two-day summit between the leaders of the world's two most powerful economies, which ended Friday, Pyongyang launched its fourth missile test of the year, in what appeared to be part of an effort to develop a nuclear-tipped missile that could strike the US mainland.
South Korea's top nuclear envoy made the comment after talks with his Chinese counterpart Wu Dawei, as the United States sent a naval strike group to the region in a show of force.
According to a Friday report by NBC, the US National Security Council has suggested to Trump and his advisors that nuclear weapons could be returned to South Korea, or that an assassination could be staged to take the life of North Korean leader Kim Jong-un.
Adm. Harry Harris, commander of U.S. Pacific Command, directed the Nimitz-class supercarrier USS Carl Vinson and its accompanying ships, including two guided-missile destroyers and a guided-missile cruiser, to sail north to the Western Pacific from Singapore on Saturday, instead of heading for Australia as originally scheduled.
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Pyongyang has repeatedly defied global warnings about conducting missile launches and testing nuclear devices.
Analysts expect the recent barrage of missiles to continue, and activities around its known nuclear test site have raised concerns North Korea may be preparing for a sixth nuclear test.
On Sunday, a North Korean Foreign Ministry official was quoted on state-run media as vowing to step up the country's defenses to protect itself from airstrikes like the USA carried out against Syria last week.
China, a traditional ally of North Korea, had previously been reluctant to corner Pyongyang too much.
While Trump has not set out a clear strategy for dealing with the isolated nation, he has criticized the administration of former President Barack Obama for its policy of "strategic patience", in the face of North Korea's ongoing efforts to develop long-range nuclear strike capability.
But convincing the North Korean leader to negotiate remains a challenge, Blinken added, suggesting the USA could try "exerting so much pressure on Kim that he changes his calculus and sees that his best path to survival is actually through negotiations", while making clear that if the North engages in denuclearization, a peace treaty is certainly possible. "If they do, that will be very good for China, and if they don't, it won't be good for anyone".
Asked about whether that is a plausible scenario, Blinken said that although it is "hard to imagine putting meaningful pressure" on North Korea without Beijing, which has significant leverage to exert economic pressure on Pyongyang, there are several unilateral steps available to Trump. "And I think even China is beginning to recognize that this presents a threat.to China's interests as well".