The Post cited parts of an analysis conducted by the Defense Intelligence Agency that says the intelligence community thinks North Korea has "nuclear weapons for ballistic missile delivery" -- including in intercontinental ballistic missiles.
The Post said the assessment's broad conclusions were verified by two US officials familiar with the analysis.
The Pentagon did not immediately respond to a request for comment.
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It was not known if North Korea has successfully tested the smaller warhead design, the Post said, though North Korea last year claimed to have done so.
The progress means North Korea is further along the path to having a deployable nuclear missile than has previously been acknowledged.
The Post also reported that another intelligence assessment estimated that North Korea now has up to 60 nuclear weapons, more than previously thought.
North Korea has alarmed the international community by the pace and progress of its missile development program, and in July leader Kim Jong-Un conducted two tests of an ICBM -- the first time he had demonstrated ICBM capability.
The first of these trials, which Kim described as a gift to "American bastards," showed the rocket had the potential range to hit Alaska.
The second rocket test last week flew even longer, with some experts even suggesting that New York could be in range.
North Korea vowed Monday that tough new UN sanctions would not stop it from developing its nuclear arsenal, rejecting talks and angrily threatening retaliation against the United States.
