State media KCNA said Kim had reviewed a previously announced plan to fire four missiles on a trajectory over western Japan, but had decided not to go ahead with the proposal for now.
The comments came after US Secretary of Defense James Mattis warned that if North Korea fired on US territory it would be "game on."
Speaking at the Pentagon Monday, Mattis told reporters: "You don't shoot at people in this world unless you want to bear the consequences."
The KCNA report Tuesday said Kim had "examined the (strike) plan for a long time and discussed it with the commanding officers in real earnest."
The statement then appears put the onus to act on Trump, saying Kim would "watch a little more the foolish and stupid conduct of the Yankees."
Contentious drills planned
The report is assumed to be referring to the US joint military drills with South Korea, known as the Ulchi-Freedom Guardian, which are scheduled to start August 21.
The annual 10-day military drills antagonize North Korea, as Pyongyang believes they are preparations for an invasion. Seoul and Washington say the exercises are defensive in nature.
"If the planned fire of power demonstration is carried out as the US is going more reckless, it will be the most delightful historic moment when the Hwasong artillerymen will wring the windpipes of the Yankees and point daggers at their necks," the report said.
The US and South Korea have confirmed the drills will go ahead as planned.
China's Global Times newspaper, a state-run tabloid, was scathing of South Korea's decision to proceed with the drills.
"The drill will definitely provoke Pyongyang more, and Pyongyang is expected to make a more radical response," it said in an editorial.
"If South Korea really wants no war on the Korean Peninsula, it should try to stop this military exercise."
The Global Times, while state-run, often uses stronger language than the official line from Beijing.
The Chinese Ministry of Foreign Affairs told CNN its official line is that "the bottom line" to resolve the North Korea nuclear issue is "to uphold the general direction of dialogue, negotiation and political settlement."
"The current situation on the Korean Peninsula is highly complex and sensitive. We hope to see the relevant sides 'extinguish fire' through their words and actions instead of 'adding fuel' amid tensions. We hope to see them improve mutual trust, and move toward the goal of preserving peace and stability on the peninsula as well as realizing the denuclearization of the peninsula."
Moon: South Korea will 'block war'
While the US and South Korea are unlikely to back down from the planned drills, South Korea President Moon Jae-in appeared to down play Mattis' comments Tuesday, pointing out the US would need its approval before launching any attack on North Korea.
In televised comments, Moon said that "military action on the Korean Peninsula can only be decided by South Korea and no one else can decide to take military action without the consent of South Korea."
"The government, putting everything on the line, will block war by all means," he added.
The address came on the anniversary of the liberation of the Korean peninsula from Japanese occupation at the end of World War II, an important holiday in both North and South Korea.
The timing of Moon's speech, a proponent of increased engagement and dialogue with his northern neighbors, was likely meant to hammer home the importance of Seoul's role in finding a diplomatic solution to the crisis, according to John Delury, a professor of international relations at Yonsei University's Graduate School of International Studies.
"It's independence day, it's a speech about South Korea's tragic history, of its fate being decided by great powers," he said. "South Korea has gotten lost in the shuffle."
Fire and Fury
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.
North Korea says it needs the weapons to deter any US-led attempts at regime change, while the United States sees a rogue state with nuclear weapons as a threat to global security.
Senior Trump administration officials have said that the US is not interested in regime change, and has no desire to "inflict harm on the long-suffering North Korean people."
President Trump discussed the crisis with Japanese Prime Minister Abe in a phone call later Monday Washington time.
"We agreed that the most important thing is not to let North Korea launch the missile," Abe told reporters after the meeting.
The next step?
Amid the heated rhetoric last week, North Korean state media said Kim had ordered senior generals to finalize a plan to fire four missiles less than 25 miles off Guam by mid-August.
Guam is home to two US military bases and is known as the "tip of the spear" when it comes to US forces in the Pacific Ocean. It's of strategic importance to the US and is the closest US territory to the Korean peninsula.
For residents of Guam life on the island appears to be moving ahead as normal. The idyllic beaches and ocean-front hotels are still packed with tourists.
Some residents received a scare early Tuesday morning time, when an "unscheduled test" of the island's emergency broadcast went off, according to the Guam Homeland Security and Civil Defense office.
Guam resident Susan Olivares Uncangco said she saw it and then "freaked out."
"I messaged my family to make sure they were okay. It was a bad experience."
The alert was sent due to human error, the department said.
So far, the island's officials have expressed confidence that the US military and its multi-layered missile defense system that operates throughout Asia will protect them.
Mattis said Monday that Washington would be able to determine "within moments" after launch whether or not a North Korean missile was headed for US territory, including Guam.
He later added that the US would "take it out" if the missile was determined to be headed for any US territory.
But he also made clear that while the military was poised to protect Guam from the North Korean military threat, a declaration of war was a decision that remains with Trump and Congress.
"War is up to the President, perhaps up to the Congress, the bottom line is we will defend the country from an attack, for us that's war, that's a wartime situation," he said.
"We will defend the country from any attack, at any time, from any quarter. Yes, that means for a lot of young troops they're going to be in a wartime situation, welcome to reality. But it's not declaring war, it's not that I'm over here Dr. Strangelove doing things like that," he added.