Story highlights Photos show Kim standing next to what the North Koreans claim is a miniaturized nuclear device

The Pentagon has taken pains to downplay the possibility

Washington (CNN) Some U.S. intelligence analysts now believe that North Korea "probably" possesses a miniaturized nuclear warhead, several U.S. officials told CNN.

The assessment has yet to become a formal consensus view of the U.S. government. But it reveals just how far along many in the U.S. believe the reclusive country has come to gaining a nuclear-tipped ballistic missile that could potentially strike the U.S.

As North Korean leader Kim Jong Un's public rhetoric has escalated in recent weeks, concern has grown inside intelligence circles that he has made progress on several fronts.

"He is determined to prove his doubters wrong," one U.S. official told CNN, even as uncertainty remains about how much progress he has actually made in his quest for nuclear missiles.

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