A defence official said in a statement on Wednesday that its nuclear programme had "long been in the full-fledged stage of miniaturisation".
However, analysts say while there is evidence the programme is advancing, it is difficult to assess its true extent.
The claim comes hours after North Korea cancelled a planned visit by the UN Secretary General Ban Ki-moon.
Mr Ban was due to visit an industrial complex in the Kaesong economic zone run jointly by the North and South and would have been the first UN chief to visit North Korea in more than 20 years.
Speaking at a forum in Seoul, he said the move was "deeply regrettable" and that no explanation was given.
North Korea previously claimed it had miniaturised a device for the nuclear test it conducted in 2013 but experts have continued to debate how far along that process it is.
Dr John Swenson-Wright, head of the Asia programme at the Chatham House think-tank, said that while there was "growing evidence of the North's increasing technical sophistication", caution was necessary in interpreting North Korea's latest statement.
Some have interpreted the latest moves, together with some recent high-profile executions, as attempts by leader Kim Jong-un to assert his authority.
The latest announcement on nuclear advances follows the publication earlier this month of pictures apparently showing a missile being launched from a submarine. Some experts have said the images may have been doctored.
Responding to the latest claims, the South Korean defence ministry urged the North to stop developing nuclear weapons.
An anonymous South Korean military official said it was believed to be true that Pyongyang had made significant progress in miniaturising its nuclear weapons.
"But South Korea and the US share the assessment that it is not at a stage where it has completed the related technology," the official told the Yonhap news agency.
North Korea has claimed it has the technology to make nuclear warheads small enough to fit on a missile.