It came in response to an unusual address the brazen dictator delivered a day earlier when he slammed Trump and vowed to "tame the mentally deranged US dotard with fire".
He added that "Trump has denied the existence of and insulted me and my country in front of the eyes of the world".
Mr Trump's executive order expanded the Treasury Department's ability to target anyone conducting significant trade in goods, services or technology with North Korea, and to ban them from interacting with the USA financial system.
Foreign minister Ri Yong Ho told reporters in NY that "it would be a dog's dream if he meant to scare us with the sound of a dog barking".
Iran unveils new long-range ballistic missile
Criticism by the Trump administration of the 2015 nuclear deal has focused heavily on Tehran's continuing missile program. The missile is named Khorramshahr after the Iranian city where the first major engagement of the war occurred.
A handful of North Korea analysts believe Kim's response - the first time he has ever released a first-person statement - could show how personally the young leader took Trump's speech. Click any of these buttons below!
"Rocket Man is on a suicide mission for himself and for his regime", Trump said, using an epithet he has recently adopted to refer to Kim Jong Un.
The country has twice successfully tested an intercontinental ballistic missile that can reach the USA, and it North Korean state media has presented images of the warhead.
Vessels and aircraft that have visited North Korea in the past 180 days are prohibited from entering USA under the new sanctions.
The fresh sanctions allow the government to cut access to the American financial system of any foreign financial company that conducts business with North Korea.
In recent months, the North has launched a pair of still-developmental ICBMs it said were capable of striking the continental United States and a pair of intermediate-range missiles that soared over Japanese territory.
TMZ: Kylie Jenner pregnant with Travis Scott's baby
However, the couple has yet to publicly confirm any pregnancy news. "She is really excited and so is Travis ", the source added. Kylie and Scott started dating shortly after she ended things with her longtime on-again off-again boyfriend, rapper Tyga .
The latest and sixth nuclear test Pyongyang conducted was Sep.
Mr Trump also said China was imposing major banking sanctions, but there was no immediate confirmation from the North's most important trading partner.
Beijing has repeatedly expressed concern about the rise of tensions over North Korea and, while it too has signed up for the increasingly tough United Nations sanctions, it has also urged a return to talks and for all parties to exercise restraint.
"It will play on a continuous loop on North Korean national television" as proof that Pyongyang needs an effective deterrent against what it views as American aggression.
CHANG: And a final jab - Kim said Trump was a dotard.
"According to a senior Japanese official, Abe said he supports and wants to cooperate with Guterres' efforts toward reform, but "(the issue of) United Nations reform will not be resolved without Security Council reform".
50 countries signed the UN's Nuclear ban treaty
Security Council seat holders - Britain, China, France, Russia and the United States - which all possess the destructive devices. However, with President Donald Trump's policy of increasing the US' defenses, the fate of START's future may now be uncertain.
However, the rhetoric was starting to rattle some in the global community.