Kim Jong-un has overseen the testing of a "new nuclear-powered underwater attack drone".
Citing North Korean media, The Times writes that the new drone could unleash a "radioactive tsunami" on naval vessels and coastal ports.
There was no confirmation of the weapons test, but some experts expressed doubts about its credibility.
However, if the claims are accurate, it would add to North Korea's status as a nuclear power and cast further doubt on the Western intent to persuade the regime to denuclearize.
"The mission of the strategic underwater nuclear weapon is to stealthily penetrate operational waters and make a radioactive tsunami through underwater detonation to destroy the enemy's naval attack groups and key operational ports," the Korean Central News Agency said.
The Times further writes: "The test correctly evaluated all tactical and technical specifications and navigational and technical indices of the underwater nuclear attack drone, verified its reliability and safety, and fully confirmed its lethal strike capability," KCNA said.
The test of the new weapon is the latest gesture of defiant retaliation against South Korea and the United States, which are conducting their largest joint military exercises in more than five years.
These include landing rehearsals, in which British troops also take part. But some analysts questioned North Korea's claims that it had achieved such an advanced weapon.
Ankit Panda, of the Carnegie Endowment for International Peace in Washington, said North Korea is more likely to use its limited supply of nuclear weapons materials, conventionally, than on an unsafe technology.
"I tend to take North Korea seriously," he tweeted, adding: "I can't rule out the possibility that this is an attempt at deception."
Meanwhile, South Korea's President Yoon said Pyongyang would pay for "reckless provocations" as he held a memorial for troops killed in border clashes with North Korea.