State media published images showing Kim Jong-un standing next to what it said was a miniaturized weapon.
The claim is impossible to verify from the images alone and experts have long cast doubt on such assertions.
North Korea has stepped up its bellicose rhetoric in response to the UN imposing some of its toughest sanctions.
The move by the Security Council came after North Korea conducted its fourth nuclear test and launched a satellite, both of which broke existing sanctions.
In recent days, Pyongyang has threatened to launch an “indiscriminate” nuclear strike on the US and South Korea, as they began their largest ever round of annual military exercises.
The drills, known as Foal Eagle and Key Resolve, routinely generate tension.
The claim from Kim Jong-un was made as he inspected a nuclear facility on March 9.
“The nuclear warheads have been standardized to be fit for ballistic missiles by miniaturizing them,” state news agency KCNA quoted Kim Jong-un as saying.
“This can be called true nuclear deterrent,” he added.
Kim Jong-un also inspected nuclear warheads designed for thermo-nuclear reaction, the type used in a hydrogen bomb, KCNA said.
If the claim is true and North Korea can put nuclear warheads on to the tips of its ballistic weapons, it would represent a clear threat to the North’s neighbors and the US.
In October 2014, the commander of US forces in South Korea, Gen. Curtis Scaparrotti, told reporters that he believed North Korea had the capability to miniaturize a nuclear device.
In May 2015, the North Korea’s National Defense Commission said the country had succeeded in miniaturizing nuclear weapons.
However, the validity of the nuclear boasts has been widely questioned. Experts also still doubt North Korea’s claim that the nuclear test it conducted in January was of a hydrogen bomb.
In addition to the new UN sanctions, which target luxury goods, financing and trade, South Korea has also announced its own measures against North Korea, which includes blacklisting individuals and entities it believes are linked to the weapons program.
The US and South Korea are currently discussing the possible deployment of a US missile defense system to the peninsula, a move strongly opposed by North Korea, Russia and China.
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