The intermediate-range missiles would be fired east and over Japan before landing around 30 to 40 kilometers (18 to 25 miles) off the coast of the tiny island if the plan is implemented, according to state-run KCNA. Guam is more than 3,000 kilometers from North Korea.
"North Korea best not make any more threats to the United States," Trump said. "They will be met with fire, fury and frankly power the likes of which this world has never seen before."
North Korea responded to Trump's comments through a state media report, criticizing the US President for having "let out a load of nonsense about 'fire and fury,'" and accused him of "failing to grasp the on-going grave situation."
The report states that "sound dialogue is not possible with such a guy bereft of reason and only absolute force can work on him."
North Korea has also slammed US and UN sanctions placed on the country over its recent increase in missile testing, and has used those measures to justify its renewed aggressiveness.
White House streamlines messaging
The sudden escalation in tensions in the past week came after US intelligence analysts assessed that North Korea had produced a miniaturized nuclear warhead, according to multiple sources familiar with the analysis of North Korea's missile and nuclear program.
Such a development would mean North Korea is a step closer to having the capability of striking the US with a nuclear-tipped missile.
There is no indication that the Hwasong-12 missiles mentioned in the Guam plan would be tipped with nuclear warheads.
The White House was accused of sending mixed messages on its North Korea stance, with Trump's fiery comments juxtaposed with US State Secretary Rex Tillerson's more diplomatic approach, which focused on dialogue.
But those messages are beginning to converge.
Tillerson on Wednesday backed Trump's comment while trying to allay fears that a military confrontation was imminent.
And US Defense Secretary James Mattis on Wednesday also supported Trump's controversial remarks.
"The DPRK should cease any consideration of actions that would lead to the end of its regime and the destruction of its people," Mattis said in a statement Wednesday, using an acronym for North Korea.
Trump's comments have been slammed as incendiary by his political opposition as well as some foreign powers, but have been supported by others.
Four rockets flying 1,065 seconds
The KCNA report includes detailed provisional plans to launch four rockets "above Shimane, Hiroshima and Koichi Prefectures of Japan," and specified they would fly 3,356 kilometers (2,000 miles) for 1,065 seconds as a "crucial warning to the US." Following that flight path, the missiles would also have to travel over the Japanese prefecture of Ehime.
North Korea's estimated splashdown of the missiles would place them just outside Guam's 12-nautical-mile territorial waters, but well within its 200-nautical-mile Exclusive Economic Zone.
The Korean People's Army Strategic Force will present the final plan for the launch to Kim by mid-August and "wait for his order," the report said.
Should Kim give the go-ahead, it would not be the first time a North Korean rocket has crossed over Japanese territory.
Japan's chief cabinet secretary, Yoshihide Suga, said that his government "can never tolerate North Korea's provocations," and urged the rogue state to comply with UN resolutions regarding its missile and nuclear programs.
Likely to follow threat through?
A South Korean military official says that there have been no indications that Pyongyang is readying a strike.
"Currently, there is no unusual movement related to a direct provocation," South Korea's Joint Chiefs of Staff spokesman Roh Jae-cheon said in a press briefing.
Some analysts do not think that Kim will follow through on this very specific threat against the US territory.
North Korea is "trying to ratchet up the threat to create political pressure in the US and elsewhere to get talks," says Carl Schuster, a Hawaii Pacific University professor and former director of operations at the US Pacific Command's Joint Intelligence Center.
"They've noticed that we've never sought conflict with an adversary who can hit our territory (and they) hope that this (threat) will force a more diplomatic line."
Meredith Sumpter, Asia director of the Eurasia Group and a long-time Asia analyst, says that despite the escalation in tensions, "we are no closer to actual military confrontation now then we were before.
"Kim Jong Un says a lot of things and he makes a lot of threats, but at the end of the day he knows that if he should undertake any kind of military strike against the US and its allies, the counter response will likely be the end of his regime," she told CNN.
A state media report Wednesday gave first signs of a Guam strike plan and mentioned a potential strike on Andersen Air Force Base, designed "to send a serious warning signal to the US."
The base is one of two on the Pacific island, which are the closest bases on US soil to North Korea. The US has flown bombers from Guam over the Korean peninsula in military drills with Japan and South Korea.
Dubbed the "tip of the spear," Guam is a key part of the US presence in the Pacific and is home to thousands of American service members and their families.
As part of its defenses on Guam, the US installed a Terminal High Altitude Area Defense (THAAD) system in 2013. The THAAD system is specifically designed to shoot down ballistic missiles.
Also, the US routinely uses Aegis-equipped warships around the island chain of the Marianas, of which Guam is the largest.