WASHINGTON—North Korea probably has the capability to produce a nuclear warhead that could be mounted on a rocket, a top U.S. commander said Friday, moving it closer to building a nuclear missile.

Speaking to reporters at the Pentagon, Gen. Curtis Scaparrotti, commander of U.S. forces on the Korean peninsula, said North Korea now is capable of building a miniaturized nuclear warhead, a step needed to complete development of a nuclear-tipped missile.

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