She also said that while the USA is "not looking for war", if Kim continues to develop nuclear weapons, "we will continue with further pressure".
"The forthcoming measures by DPRK [the Democratic Republic of Korea] will make the U.S. suffer the greatest pain it has ever experienced in its history", he told a United Nations conference in Geneva.
But on Sunday night USA officials appeared to tone down their demands, scrapping the asset freeze and softening restrictions on North Koreans working overseas.
Recent months have seen an alarming escalation in tensions between the isolated Korean state and the U.S., with Pyongyang launching increasingly ambitious missile tests and Mr Trump promising "fire and fury" in response.
According to North Korea, the U.S. "is trying to use Pyongyang's legitimate self-defensive measures as an excuse to strangle and completely suffocate it". An Aug. 5 United Nations resolution banned North Korean exports of coal.
The initial text included a total ban on oil imports, a measure seen by some analysts as potentially destabilising for the regime. Additionally, other countries now can not issue work permits to North Korean labourers and firms can not indulge in joint ventures with the nation either.
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Washington's "scheme" to hamper Pyongyang's development and disarm the country through sanctions and pressures "has become clearly evident" through the passage of the new resolution, the North added. The DPRK stands for the Democratic People's Republic of Korea, North Korea's official name.
The resolution, adopted in response to Pyongyang's sixth and strongest nuclear test explosion, bans North Korea from importing all natural gas liquids and condensates.
NBC News reports even more rhetoric, this time from North Korea's ambassador to the U.N., Han Tae Song, who rejected and condemned the sanctions (calling them "illegal and unlawful") and says that the USA should be prepared for the "greatest pain".
A defiant North Korea condemned Tuesday the latest round of UN sanctions against the country and warned the United States of "forthcoming measures" by the hands of the secretive state. "The North Korean regime has not yet passed the point of no return", she also said.
Following the vote, U.S. Ambassador to the United Nations Nikki Haley portrayed North Korea as increasingly isolated.
That would amount to a 10 percent cut in oil products, according to the US Energy Information Administration, which estimates annual exports to North Korea at almost 2.2 million barrels.
Previous sanctions stopped short of imposing controls on oil and fuel.