NEW YORK — President Donald Trump added economic action to his fiery military threats against North Korea on Thursday, authorizing stiffer new sanctions in response to the Koreans’ nuclear weapons advances.

North Korean leader Kim Jong Un issued a rare statement, branding Trump as “deranged” and warning he will “pay dearly” for his threat to “totally destroy” the North if it attacks.

The exchange of super-heated rhetoric and unusually personal abuse between the adversaries will escalate tensions that have been mounting as North Korea has marched closer to achieving a nuclear-tipped missile that could strike America. The crisis has dominated Trump’s debut at this week’s annual U.N. General Assembly meeting.

Kim’s statement, carried by North Korea’s official news agency, responded to Trump’s combative speech where he not only issued the warning of potential obliteration for the isolated nation, but also mocked the North’s young autocrat as a “Rocket Man” on a “suicide mission.”

Kim offered choice insults of his own. He said Trump was “unfit to hold the prerogative of supreme command of a country.” He described the president as “a rogue and a gangster fond of playing with fire.” He characterized Trump’s Tuesday speech to the world body as “mentally deranged behavior.”

“I will make the man holding the prerogative of the supreme command in the U.S. pay dearly for his speech calling for totally destroying the DPRK (Democratic People’s Republic of Korea),” said the statement carried by Korean Central News Agency.

On Thursday, Trump announced the latest steps to punish foreign companies that deal with the North, the latest salvo in a U.S.-led campaign to isolate and impoverish Kim’s government until it halts missile and nuclear tests. He announced the measures as he met leaders from South Korea and Japan, the nations most immediately imperiled.