Stavridis said that he hopes that Kim follows the "correct course of action here, which is to stand down at the idea that he's going to launch missiles at the United States".
Chinese Foreign Minister Wang Yi vowed after the United Nations sanctions were approved that his country "will for sure implement that new resolution 100 percent, fully and strictly".
Kim visited the Korean People's Army as the self-imposed mid-August deadline for a missile demonstration approached, the Korean Central News Agency reports.
He later added that the USA military is "locked and loaded" to respond to its provocations. It does mean working to induce North Korea's military and political elites to depose the dictator.
Instead, at the recent ASEAN security summit in the Philippines, Tillerson indicated the USA would be open to talks if North Korea merely stopped the missile launches.
South Korean Vice Defence Minister Suh Choo-suk highlighted doubts about North Korea's claims about its military capability.
North Korea says it was compelled to put the Guam plan together because it feels threatened by a squadron of B-1B bombers on the island that the USA has increasingly sent to fly in Korean airspace in symbolic shows of force during times of particular tension.
"It's independence day, it's a speech about South Korea's tragic history, of its fate being decided by great powers", he said.
Tension in the region has risen since North Korea carried out two nuclear bomb tests previous year and two intercontinental ballistic missile tests in July, tests it often conducts to coincide with important national dates.
North Korean leader Kim Jong-un on Monday called off a threatened missile strike against the USA territory of Guam in the Pacific, quelling fears of a potential military confrontation.
North Korea has said its military presented leader Kim Jong Un with plans to launch missiles into waters near Guam.
"The alternative would have been both catastrophic and unacceptable!"
One large map appeared to show a straight line between northeastern North Korea and Guam, a U.S. territory in the western Pacific that is home to American military bases.
The US and North Korea have been engaged in increasingly threatening rhetoric since last Tuesday when US bombers flew over the Korean peninsula, and US President Donald Trump threatened Pyongyang with "fire and fury" following an assessment that North Korea had miniaturized a nuclear warhead. These facts have made the South Koreans a tad uneasy with the prospect of a war- conventional or nuclear.
On Tuesday, China, North Korea's closest diplomatic ally, urged Washington and Pyongyang to "put the brakes" on all provocative actions and statements.
North Korea regards the USA exercises with South Korea and Japan as preparations for invasion.
The missile plans were previously announced.
But Mr Kim said he would "watch a little more the foolish and stupid conduct of the Yankees" before executing any order.
"Whatever ups and downs we face, the North Korean nuclear situation must be resolved peacefully", South Korean President Moon Jae-in told a meeting with senior aides and advisers. A miscalculation on either side could lead to military confrontation. The current approach can be improved if we make it clear to North Korea that we are more than willing to take military action.
Citing a military general, it said North Korea would shortly develop a plan for launching four missiles over Japan and into the waters near Guam, where the U.S. has a large military presence. It would be a test of the Hwasong-12, a new missile the country flight-tested for the first time in May.
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