The USS Carl Vinson will be joined by the Ashigara and Samidare destroyers in "tactical training" drills near the Philippines, the Japan Maritime Self Defense Force said.
North Korea's state-run newspaper Rodong Sinmun said in an editorial the country is ready to illustrate its "military force" by sinking a "nuclear-powered aircraft carrier with a single strike."
The state newspaper claimed to have weaponry which "can reach continental US and Asia Pacific region" and the "absolute weapon," hydrogen bomb.
CNN cannot independently verify the claims.
In the face of recent saber-rattling from North Korea, US President Donald Trump had said the Vinson carrier group was being deployed to waters off the Korean Peninsula
The location of the Vinson has dominated headlines after Trump's remark on April 12.
Trump said he was sending "an armada" to Korean waters potentially to deal with threats from North Korea. The statement came after Pyongyang said it had successfully launched a new ballistic missile.
"We are sending an armada. Very powerful," Trump told Fox Business Network's Maria Bartiromo
. "We have submarines. Very powerful. Far more powerful than the aircraft carrier. That I can tell you."
But it turned out the carrier group was not actually steaming toward the peninsula, but rather heading to joint exercises with the Australian navy.
The US Pacific Command said Tuesday that training with the Australian navy had been completed, and that "the Carl Vinson Strike Group is heading north to the Western Pacific as a prudent measure."
US defense officials told CNN the Vinson and its carrier group would arrive off the Korean Peninsula by the end of April.
Sunday's threats are consistent with others North Korea has made in past weeks. North Korea has said it will respond in kind to any US attack on the country. And it has claimed it would strike the US mainland and US carriers and forces in the region, specifically US bases in South Korea and Japan.