CNN cannot independently verify the claims.

President Donald Trump has pledged to rein in the "menace" of North Korea's nuclear program, and has spoken to Chinese President Xi Jinping about getting China, as one of North Korea's only allies, to put pressure on its neighbor to change course.

Phone calls

Trump spoke by phone with Xi and Prime Minister Shinzo Abe of Japan Sunday night Washington time, the White House said. North Korea came up in both conversations.

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.