In a third day of fiery rhetoric, the North said: "Sanctions mean a declaration of war against us."
The reclusive regime this week declared a boycott of all dialogue aimed at ending its atomic programme and vowed to conduct more rocket and nuclear tests after the UN Security Council censured it for a long-range missile launch in December.
"If the puppet group of traitors takes a direct part in UN sanctions, the Democratic People's Republic of Korea will take strong physical counter-measures," the North's Committee for the Peaceful Reunification of Korea said, referring to the South.
Speaking in Beijing, the United States' special representative for North Korea policy, Glyn Davies, said North Korea's rhetoric was "troubling", and added he and his Chinese counterparts agreed a nuclear test would be harmful.
"We will judge North Korea by its actions, not its words. These types of inflammatory statements do nothing to contribute to peace and stability," he said.
"What North Korea has done through its actions – in particular through the launch on December 12 of a rocket, in contravention of UN Security Council resolutions – is they have made it much more difficult to contemplate getting back to a diplomatic process."
The UN Security Council this week unanimously condemned the rocket launch and expanded its existing sanctions on North Korea.
The US wanted a resolution imposing entirely new sanctions against Pyongyang, but Beijing rejected that option. China agreed to UN restrictions after North Korea's 2006 and 2009 nuclear tests.
On Thursday, the US placed economic sanctions on two North Korean bank officials and a Hong Kong trading company it accused of supporting Pyongyang's proliferation of weapons of mass destruction.
The company, Leader (Hong Kong) International Trading Ltd, was separately blacklisted by the UN this week.
Seoul has said it will look at whether there are any further measures it can implement alongside the US, but said the focus for now is to follow Security Council resolutions.
North Korea's rhetoric this week amounted to some of the angriest outbursts against the outside world under the leadership of Kim Jong-un, who took over after the death of his father Kim Jong-il in late 2011.
On Thursday, the North said it would carry out further rocket launches and third a nuclear test, directing its ire at the US, a country it called its "sworn enemy".
US Defence Secretary Leon Panetta said the comments were worrying.
North Korea is not believed to have the technology to deliver a nuclear warhead capable of hitting the continental United States, although its December launch showed it had the capacity to deliver a rocket that could travel 6200 miles, potentially putting San Francisco in range, according to an assessment by Seoul.
South Korea and others who have been observing activities at the North's known nuclear test grounds believe Pyongyang is technically ready to go ahead with its third atomic test.
The North has also declared a landmark agreement it signed in 1992 on eliminating nuclear weapons from the Korean peninsula was invalid, repeating its long-standing accusation that Seoul was colluding with Washington.
China's foreign ministry has repeated its call for calm on the Korean peninsula.