Kim Jong-un has said remarks by "deranged" US President Donald Trump have convinced him he is right to develop weapons for North Korea.
In an unprecedented personal statement, via state media, Mr Kim said Mr Trump would "pay dearly" for his recent speech to the UN.
The US president said on Tuesday that if America was forced to defend itself it would "totally destroy" North Korea.
Mr Trump also mockingly called Mr Kim a "rocket man" on a "suicide mission".
The two countries have been engaging in increasingly heated rhetoric in recent months.
North Korea has been testing missiles at an unprecedented rate, and conducted its sixth nuclear test despite international condemnation.
North Korean Foreign Minister Ri Yong-ho, who had earlier compared Mr Trump's speech to "the sound of a barking dog", has warned that Pyongyang could test a hydrogen bomb in the Pacific Ocean in response to the US president's threat.
"It could be the most powerful detonation of an H-bomb in the Pacific," Mr Ri said, quoted by South Korea's Yonhap news agency.
However, he added: "We have no idea about what actions could be taken as it will be ordered by leader Kim Jong-un."
Mr Trump on Thursday signed a new order boosting sanctions against North Korea, where the US treasury would target firms and financial institutions doing business with Pyongyang.
He said: "For much too long North Korea has been allowed to abuse the international financial system to facilitate funding for its nuclear weapons and missile programs."
The US president also said China's Central Bank had instructed other Chinese banks to stop doing business with Pyongyang, but this has not been confirmed by Beijing.
The UN Security Council had approved new rounds of sanctions earlier this month aimed at starving North Korea of fuel and income, which were in response to Pyongyang's much-condemned sixth nuclear test on 3 September.
North Korea was one of the top issues dominating the agenda at the UN General Assembly in New York, where several speakers called for a de-escalation of tensions.
Russian Foreign Minister Sergei Lavrov warned that "military hysteria" over the nuclear testing would lead to "disaster", while China's Foreign Minister Wang Yi told Pyongyang not to go in a "dangerous direction".
Mr Wang told the UN on Thursday that there should be no new nuclear weapons on the Korean peninsula "whether it is in the North or the South".