"We call on (North Korea) to refrain from provocative, destabilizing actions and rhetoric, and to make the strategic choice to fulfill its international obligations and commitments and return to serious talks," Pentagon spokesman Gary Ross said. "North Korea's unlawful weapons programs represent a clear, grave threat to US national security."
The statement came just hours after a North Korean newspaper said Pyongyang was ready to take out a US aircraft carrier conducting drills with Japanese destroyers near the Philippines.
Rodong Sinmun, the official newspaper of the North Korean government's Central Committee, said in an editorial the country is ready to illustrate its "military force" by sinking the "nuclear-powered aircraft carrier with a single strike."
The newspaper claimed Pyongyang has weaponry that "can reach continental US and Asia Pacific region" and the "absolute weapon," a hydrogen bomb.
CNN cannot independently verify the claims.
North Korea conducted its fifth nuclear weapons test last September and displayed a series of missiles at a military parade on an important North Korean holiday earlier this month before firing one off, which the US said went down in flames shortly after the launch.
President Donald Trump has pledged to rein in the "menace" of North Korea's nuclear program, and has spoken with Chinese President Xi Jinping several times about getting China, as one of North Korea's only allies, to put pressure on its neighbor to change course.
The State Department said Sunday that it remains committed to directly addressing the North Korean nuclear threat.
"Provocations from North Korea have grown far too common and far too dangerous to ignore," a department spokesperson said, referring to the country by the acronym for its official name, the Democratic People's Republic of Korea. "Together with the international community, we will hold the Kim Jung-un regime accountable for its dangerous and reckless actions and serious human rights abuses through a robust international campaign to cut the DPRK off from the rest of the world through diplomatic, security, and economic measures.
"With our allies and partners around the world, we will show the DPRK that the only path to a secure, economically-prosperous future is to abandon its nuclear and ballistic missile programs," the spokesperson said.
"We do not seek military conflict, nor do we seek to threaten North Korea," the spokesperson added. "However, we will respond to threats to us or our allies accordingly. We remain open to talks with the DPRK, but need to see that the DPRK will cease all its illegal activities and aggressive behavior in the region."
The US said Tuesday that it was sending the USS Carl Vinson towards North Korea and that the strike group that it leads would reach there by late April.
The Pentagon spokesman, Ross, said the US continued commitment to defending South Korea and Japan was "ironclad."
Homeland Security Secretary John Kelly said in an interview on CNN's "State of the Union" on Sunday that a North Korean nuclear missile capable of striking the US would be a "grave threat" and anticipated North Korea could achieve this capability before Trump would begin his second term.
Sunday's threats from Pyongyang are consistent with others North Korea has made in past weeks. The country has said it will respond in kind to any US attack, and it has warned it would strike the US mainland and US carriers and forces in the region, specifically US bases in South Korea and Japan.