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SEOUL, South Korea — North Korea said on Sunday that it has developed a hydrogen bomb “with super explosive power” to be mounted on its intercontinental ballistic missile.

The North’s official Korean Central News Agency offered no evidence for the claim, other than photos of Kim Jong-un, the country’s leader, inspecting what it said was the weapon. The report said Mr. Kim had visited the Nuclear Weapons Institute, which the news agency said had recently “succeeded in a more developed nuke” and in “bringing about a signal turn in nuclear weaponization.”

“He watched an H-bomb to be loaded into new ICBM,” the news agency reported, without revealing when Mr. Kim’s visit took place.

The news agency’s photographs showed a sign saying that the bomb, if it was one, was meant for the Hwasong-14 intercontinental ballistic missile, which North Korea flight-tested twice in July.

In its fourth nuclear test, conducted in January 2016, North Korea claimed to have detonated its first hydrogen bomb. But most analysts disputed the claim, saying that the explosive yield was too small to be from such a device, which would be far more powerful than the atomic bombs it had previously tested.

In North Korea’s second intercontinental ballistic missile test, on July 28, the Hwasong-14 demonstrated the potential to reach the lower 48 United States. But South Korean officials and analysts have said that North Korea has yet to master the so-called re-entry technology needed for a nuclear warhead to survive intense heat and friction as the missile plunges through the earth’s atmosphere from space.

On Sunday, the North Korean report said the hydrogen bomb had an explosive power adjustable from tens of kilotons to hundreds of kilotons. It described the weapon as “a multifunctional thermonuclear nuke with great destructive power which can be detonated even at high altitudes” to launch an electromagnetic pulse, or EMP, attack. An EMP attack can destroy electronic devices in a vast area of enemy territory.

Hours after the North’s announcement, the White House said in a statement that President Trump had discussed “the growing threat from North Korea” with Prime Minister Shinzo Abe of Japan. The statement did not say whether the conversation took place before or after the North Korean announcement.

Over the years, some nuclear experts have said that even if North Korea has not developed a true thermonuclear, or hydrogen, bomb, it may have increased the yield of a more traditional nuclear device by using tritium, a common enhancement technique.

A hydrogen bomb is a highly sophisticated weapon capable of achieving thousands of kilotons of explosive yield. In comparison, the last and most powerful of North Korea’s five nuclear tests, conducted in September 2016, produced an explosive yield of only 10 to 15 kilotons, about the same as the nuclear blast in Hiroshima, Japan, at the end of World War II, according to officials and analysts.

“North Korea appears to have a family of relatively reliable, miniaturized fission weapons with the destructive force rivaling the size of the Hiroshima blast that can use plutonium or weapon-grade uranium and fit on a number of ballistic missiles,” David Albright, president of the Washington-based Institute for Science and International Security, said during congressional testimony last September.

But Mr. Albright said “it is reasonable to skeptically accept that North Korea is working on some type of thermonuclear device, likely one aimed at using thermonuclear materials to significantly boost the yield of a fission device.” His institute has predicted that “in a worst-case assessment,” North Korea could field a crude thermonuclear weapon with a yield approaching 100 kilotons soon after 2020, or possibly sooner.

North Korea’s claim came just days after it sent a ballistic missile over Japan, escalating recent tensions over its pursuit of nuclear missiles. Mr. Trump has threatened to unleash “fire and fury” on the North if it continues to threaten the United States with a nuclear weapon.

Bombastic threats and exaggerated claims have long been part of North Korea’s domestic propaganda and its strategy for dealing with its enemies. But some analysts said that the outside world has long underestimated Pyongyang’s determination to build a reliable nuclear force and needed to pay more attention to its latest claim.

“Disbelieve at your own peril,” said Lee Sung-yoon, a Korea expert at the Fletcher School of Law and Diplomacy at Tufts University. “Trump should remember: It took China only three years to go from its first atom bomb test, in 1964, to to its first hydrogen bomb test, in 1967, 50 years ago.”

But high-ranking United States officials have said that North Korea still has key obstacles to overcome before it can field a nuclear-tipped intercontinental ballistic missile capable of threatening the American mainland.

“It is clear North Korea has the capability to build a missile that can range the distance to the United States, but North Korea has yet to demonstrate it has the requisite technology and capability to actually target and strike the United States with a nuclear weapon,” Gen. Paul Selva, vice chairman of the Joint Chiefs of Staff, recently told Bloomberg News.

First, North Korea would have to deploy a guidance and stability control system that can direct a long-range missile accurately over thousands of kilometers without the missile breaking apart, General Selva said. Second, the North needs a re-entry vehicle housing the warhead that can survive the heat and stresses of an intercontinental ballistic launch. Third, he said, it needs a nuclear weapon “that is small enough and stable enough to survive the trip.”

North Korea has accelerated its missile and nuclear tests since Mr. Kim took power in 2011. This year alone, it has conducted 14 missile tests, and analysts expect more. Some have speculated that the North may conduct a nuclear test or a significant missile test on Saturday, a national holiday.

Mr. Kim said on Wednesday that the missile launch over Japan could be a “curtain raiser” for more such tests in the Pacific. He has threatened to fire missiles into waters around Guam, an American territory that is home to Andersen Air Force Base. In a show of force, two B-1B Lancer bombers took off from the base on Thursday to participate in joint bombing drills in South Korea.