The unclassified version of the report, which was required by a 2012 law, offered no estimate of when North Korea might achieve that capability.
It said the pace of progress will depend in part on how many resources are invested.
The report fits an established US intelligence picture of North Korea making an enormous effort to become a nuclear power and of an economically poor country directing a disproportionate amount of resources to its military.
The Pentagon report said the US foresees little change in North Korea's key strategic aims, which it said to include using "coercive diplomacy" to compel acceptance of its security interests, as well as developing a nuclear arsenal and undermining of the US-South Korean alliance.
"We anticipate these strategic goals will be consistent under North Korea's new leader, Kim Jong Un," it said.
US intelligence agencies are not fully in agreement on how far North Korea has advanced in its effort to make a nuclear weapon small enough to fit atop a ballistic missile.
The DIA assessment did not mention the potential range of such a strike.
Director of National Intelligence James Clapper, the top US intelligence official, said shortly after the DIA assessment was made public that its conclusion was not shared by other intelligence agencies.
Clapper said North Korea has made progress but has not "fully developed, tested or demonstrated the full range of capabilities necessary for a nuclear-armed missile."
In its report yesterday, the Pentagon made no mention of the DIA report.
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