He added that Trump was "unfit to hold the prerogative of the supreme command of a country".
"Now that Trump has... made the most ferocious declaration of a war in history that he would destroy the DPRK, we will consider with seriousness exercising of a corresponding, highest level of hard-line countermeasure in history", Kim was quoted by the KCNA as saying.
Saturday's seismic activity came just hours before North Korea's Foreign Minister Ri Yong Ho - who warned on Thursday that North Korea could consider a hydrogen bomb test of an unprecedented scale over the Pacific - was due to address the United Nations General Assembly in NY.
North Korea has long said that its weapons tests are necessary because of USA hostility, which for Pyongyang includes the almost 80,000 US troops stationed in Japan and South Korea. She called on world powers to toughen their approach to President Kim Jong-un's actions.
Believe it or not, Kim's statement actually used gentler language than his propaganda specialists have favored in the past. North Korean state TV later showed a solemn-looking Kim, dressed in a gray Mao-style suit, reading the statement.
President Donald Trump is meeting with South Korean President Moon Jae-in on Thursday about the ongoing North Korea crisis.
A USA government intelligence analyst said the events could have been a "mine-type" collapse of tunnels damaged by North Korea's previous nuclear test, but was more likely a small natural disaster. On Thursday, the US unveiled its own set of economic sanctions targeting North Korea.
The quake was detected in an area around Kilju, in northeastern North Korea, just 6 kilometers (3.7 miles) northwest of where the North conducted its sixth and most powerful nuclear test on September 3, according to an official from Seoul's Korea Meteorological Administration.
The order was created to dissuade Pyongyang from pursuing its nuclear missile program.
Tensions have continued to rise since North Korea carried out its sixth nuclear test on 3 September, prompting a new round of United Nations sanctions.
Numerous scientific agencies on both sides of the Pacific detected an quake Saturday near the site where North Korea set off a hydrogen bomb earlier this month, at first prompting speculation of another weapons test, before a consensus appeared to emerge that the tremor was a natural occurrence. "You are protected. Nobody's going to mess with our people". "We are talking about putting a live nuclear warhead on a missile that has been tested only a handful of times. It is truly terrifying if something goes wrong".
The ongoing war of words between the two leaders on opposite sides of the Pacific have been exacerbated in recent months amid growing tension over North Korea's nuclear weapons build-up.
Foreign banks "can choose to do business with the United States or with North Korea but not both".
In the course of the speech, Trump said if the United States is "forced to defend itself and its allies, we will have no choice but to totally destroy North Korea".
Here's the key line in Kim's argument: "His (Trump's) remarks which described the USA option through straightforward expression of his will have convinced me, rather than frightening or stopping me, that the path I chose is correct and that it is the one I have to follow to the last".
Mr Trump yesterday announced a new order to help the USA target people, companies and banks financing and facilitating trade with North Korea.
Anthony Ruggiero with the Foundation for Defense of Democracies think tank said of Trump's order: "This approach worked with Iran as companies, banks, governments and individuals chose the United States, and likely will restrict North Korea's revenue".
North Korea has little energy production of its own, but does refine some petroleum products from crude oil it imports - which is not included in the new ban.
Mr Trump said "tolerance for this disgraceful practice must end now".
He added, "The president obviously takes the responsibility of the security of the American people very seriously".
Tensions have continued to rise since North Korea carried out its sixth nuclear test, prompting a new round of United Nations sanctions.