SEOUL >> North Korea said Wednesday that it had already built nuclear weapons small enough to be carried by missiles, even as a senior U.S. general questioned the country’s recent claim that it had successfully tested a submarine-launched ballistic missile.

“It is long since the DPRK’s nuclear striking means have entered the stage of producing smaller nukes and diversifying them,” the National Defense Commission said in a statement, using the initials of North Korea’s formal name, the Democratic People’s Republic of Korea.

The statement was carried by the official news agency, KCNA.

“The DPRK has reached the stage of ensuring the highest precision and intelligence and best accuracy of not only medium- and short-range rockets, but long-range ones,” the agency said.

Officials and analysts in Washington and Seoul remain uncertain and even divided over how close North Korea has come to acquiring a nuclear weapon small enough to be put on a missile, or its ability to deliver a nuclear warhead on an intercontinental ballistic missile. But their concern has grown since the North placed a satellite into orbit in December 2012, successfully demonstrating a rocket technology needed for a long-range missile.

In February 2013, North Korea also claimed that it had conducted its third underground nuclear test with “a smaller and lighter A-bomb.”

A month later, the North’s main government newspaper, the Rodong Sinmun, quoted a North Korean general as saying that the North’s “intercontinental ballistic missiles and other missiles are on a standby, loaded with lighter, smaller and diversified nuclear warheads.”

Adm. William E. Gortney, the commander of the North American Aerospace Defense Command, told reporters last month that U.S. intelligence officials believed that North Korea had the ability to put a nuclear weapon on its KN-08 intercontinental ballistic missile “and shoot it at the homeland,” although he said the North had yet to run a flight test of the missile.

North Korea’s statement Wednesday came in response to international criticism of a ballistic missile test Pyongyang said it conducted May 8. U.N. resolutions prohibit North Korea from testing such a missile.

North Korea said the May 8 test involved successfully launching a strategic missile from a submarine. But some analysts questioned the claim, saying photographs may have been altered and that the test launch may have been conducted from a submerged barge.

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