Foreign Ministry spokesperson Hua Chunying made the remarks in response to the UN Security Council's new resolution against North Korea.
Condemning the North's test of an intercontinental ballistic missile on November 29, the 15-member U.N. Security Council slapped the regime with caps on its imports of refined and crude oil, and blocked key sources of revenue suspected of funding the weapons programs.
The resolution bans almost 90 percent of refined petroleum exports to the country.
US President Donald Trump has been trading open insults with North Korean leader Kim Jong-un this year, saying he would "totally destroy" North Korea. "It should also give up dreams that we will abandon our nuclear weapons", the ministry said.
North Korea said its weapons programmes are designed for self-defence against "hostile" U.S. policies towards the isolated but nuclear-armed nation. "The US should not forget that the Democratic People's Republic of Korea has rapidly emerged as a strategic state capable of posing a substantial nuclear threat to the US mainland".
North Korea said those who voted for the sanctions would face its wrath. "We will make sure for ever and ever that they pay heavy price for what they have done", the foreign ministry statement said, in characteristically bellicose language. The UN's top envoy to North Korea, Jeffrey Feltman, said this month that he was "deeply worried" about the prospects of a diplomatic solution to the crisis after meeting officials in Pyongyang.
The North's old allies China and Russian Federation both supported the latest United Nations sanctions.
He also threatened that other countries that voted in favor of the sanctions can not avoid paying a "heavy price for what they have done".
USA diplomats have made clear they are seeking a diplomatic solution but proposed the new, tougher sanctions resolution to ratchet up pressure on North Korea's leader.
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