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"North Korea's threats are not helpful. We have consistently called on North Korea to improve its relations with its neighbors, including South Korea," White House spokesman Joshua Earnest said.
Such "provocative rhetoric, these kinds of actions are just not going to improve conditions for the North Korean people," agreed State Department spokeswoman Victoria Nuland.
"They're not going to end the isolation. They're just going to increase tensions, and it's extremely regrettable."
Angered by tough new UN sanctions, North Korea has also threatened a "pre-emptive nuclear attack" against the United States and South Korea -- a notion dismissed as bluster by analysts.
But despite the reaction from Pyongyang, Washington stood by the new UN sanctions regime agreed after North Korea carried out a nuclear test last month, Nuland said.
The resolution adopted Thursday by the 15-member Council tightened restrictions on North Korea's financial dealings, notably its suspect "bulk cash" transfers.
"If we don't, as an international community, meet these provocations firmly, then we're just giving license for the will of the UN Security Council to be flouted," Nuland said.
"We've got to be firm. When we say there are consequences, there have to be consequences."
As for Pyongyang's vow to discard the 1953 armistice agreement that ended Korean War hostilities, the Pentagon said such a move would carry no legal weight.
"As a legal matter, no party to the armistice can unilaterally terminate or alter the terms of the Armistice Agreement," spokesman George Little said in an email.
While North Korea is considered unable to stage a nuclear strike on the US mainland, there are fears it could launch some provocation in the form of a missile test or artillery assault.
But Little said the US military was prepared for any potential North Korean attack.
"The United States is fully capable of defending itself and our allies against a DPRK (Democratic People's Republic of Korea) attack. We are firmly committed to the defense of the Republic of Korea and Japan," he said.