The angry statement from Pyongyang's foreign ministry came as the crisis surrounding the reclusive state was set to dominate the annual UN gathering of world leaders.
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The UN Security Council last week imposed a new raft of sanctions on North Korea, slapping an export ban on textiles, freezing work permits to North Korean guest workers and placing a cap on oil supplies.
The international community is scrambling to contain an increasingly belligerent Pyongyang, which has conducted its sixth and largest nuclear test and fired long-range missiles over Japan that it says could reach the US mainland.
Pyongyang says it needs nuclear weapons to protect itself from US forces. It says it is determined to build a weapons system capable of delivering a nuclear warhead capable of hitting the American mainland.
The state news agency KCNA, quoting the foreign ministry statement, said the economic restrictions -- which US officials estimate could deny the impoverished state more than $2 billion in revenue -- were an "act of hostility to physically exterminate the people of" North Korea.
"The increased moves of the US and its vassal forces to impose sanctions and pressure on the DPRK will only increase our pace towards the ultimate completion of the state nuclear force," it said, referring to the country by the initials of its official name.
The effectiveness of the sanctions depends largely on whether China, North Korea's ally and main economic partner, will fully implement them.
US President Donald Trump, who was was due to address the UN in New York Tuesday, spoke by phone to his Chinese counterpart Xi Jinping Monday, with the White House saying the two men were committed to "maximising pressure on North Korea."
The US flew four F-35B stealth fighter jets and two B-1B bombers over the Korean peninsula on Monday in a blunt show of force.
Trump says he has not ruled out a military option in the crisis. War could leave millions of people in the South Korean capital of Seoul -- and 28,500 US soldiers stationed in the South -- exposed.
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