In his first address to the United Nations as US President, Trump said that the US was ready to "totally destroy" North Korea if it was forced to defend its allies, a warning seen as unprecedented for a US president delivering an address to the world's leaders and top diplomats.
"I will make the man holding the prerogative of the supreme command in the USA pay dearly for his speech calling for totally destroying the DPRK", said the statement carried by Korean Central News Agency.
Trump vowed this week to "totally destroy" the nation if North Korea's tests continued, referring to Kim as "Rocket Man".
On Thursday, Trump signed an executive order permitting the U.S.to sanction individual companies and institutions that do business with North Korea.
Trump had earlier threatened Pyongyang with "fire and fury".
Pyongyang conducted its sixth and largest nuclear test on September 3 and has launched dozens of missiles this year as it accelerates a program aimed at enabling it to target the United States with a nuclear-tipped missile.
His foreign minister, asked while in NY for the U.N. General Assembly what the countermeasure would be, said his country may test a hydrogen bomb in the Pacific Ocean.
Earlier this week, U.S. President Donald Trump used powerful language to warn North Korea.
The newspaper Newsday said Mr. Trump was "taunting" Kim and the words were "startling".
Deterring Kim Jong-un from using nuclear weapons is like attempting to "deter someone on death row with the threat of execution", Dave Ochmanek of Rand Corp. told an audience at Modern Day Marine 2017.
He said Mr. Trump's remarks "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".
"North Korea's nuclear programme is a grave threat to peace and security in our world, and it is unacceptable that others financially support this criminal, rogue regime", Trump said in a press briefing with the leaders of South Korea and Japan. Below id the full text of the statement believed to be the first to be issued directly under the name of any North Korean leader.
The United States military, however, operates under the assumption that North Korea already has the capability.
South Korea, Russia and China all urged calm.
He further said, "It is time for North Korea to realise that de-nuclearisation is its only acceptable future".
"As far as I know, what you have mentioned just now is not consistent with the facts", spokesman Lu Kang said at a regular news conference.
Though the majority of North Korea's imports come from China, Treasury Secretary Steve Mnuchin said "This action is directed at everyone" and the steps are "in no way specifically directed at China".