(CNN) North Korea said Wednesday that it has the ability to miniaturize nuclear weapons, a key step toward building nuclear missiles.

Analysts and U.S. officials have said previously that they suspected Kim Jong Un 's regime was working toward accomplishing the technical feat, which is needed to fit a nuclear device on the tip of a ballistic missile.

U.S. expresses doubt

But on Wednesday, the official U.S. response was skepticism.

"Our assessment of North Korea's nuclear capabilities has not changed," National Security Council spokesman Patrick Ventrell said in a statement. "We do not think that they have that capacity."

"However, they are working on developing a number of long range missiles, including intercontinental ballistic missiles, that could eventually threaten our allies and the homeland," the U.S. spokesman added. "That is why the Administration is working to improve regional and homeland missile defenses and continuing to work with the other members of the six-party talks to bring North Korea back into compliance with its nonproliferation commitments."

The six-party talks refer to nuclear disarmament efforts by the United States, North Korea, South Korea, China, Japan and Russia.

But the North Korean assertion was unequivocal.

"We have had the capability of miniaturizing nuclear warheads, as well as producing multiform weapons, for some time," the North Korean military said in a statement carried by the state-run Korean Central News Agency.

"We can also guarantee the accuracy not only of short-to-mid-range but also long-range rocket launches, for which we have had the technology for a long time," the statement said.

Claim echoes U.S. military assessments

Despite the U.S.' official skepticism, Pyongyang's announcement about miniaturization -- the first time it has publicly made such a claim -- tallies with some recent assessments from senior U.S. military officials.

U.S. Army Gen. Curtis Scaparrotti, the commander of U.S. forces in Korea, said in October that he thought North Korea was capable of miniaturizing a nuclear device.

And Adm. Bill Gortney, the commander of North American Aerospace Defense Command, told reporters last month that the U.S. military believed that Pyongyang could put a nuclear weapon on a road-mobile missile and "shoot it at the (U.S.) homeland."

Gortney added, though, that the United States doesn't think that the missile in question, the KN-08, has been tested. And he said he was confident U.S. defenses would be able to intercept any potential North Korean attack.

Analysts suspect North Korean nuclear advances

Gauging the progress of North Korea's nuclear weapons program is a tricky business. Kim's regime generally cloaks its efforts in secrecy and occasionally trumpets claims of advances through propaganda outlets, leaving the rest of the world to try to connect the dots.

Analysts have said that North Korea may well already be able to fit nuclear warheads on ground-launched missiles that can reach South Korea and Japan.

David Albright, a former U.N. weapons inspector, recently told CNN that Pyongyang could have 10 to 15 nuclear weapons at this point and that it could grow that amount by several weapons per year.

Fashioning a nuclear device small enough to fit on the tip of a ballistic missile is difficult. North Korea signaled its intent to achieve that goal at the time of its most recent nuclear test, in 2013. It described the device it tested then as "a smaller and lighter" bomb than the ones it detonated in 2006 and 2009.

Albright said he thinks Pyongyang can miniaturize a warhead for shorter missiles, but not yet for intercontinental ballistic missiles, or ICBMs.

"There's just too much testing they need to do, to make sure the re-entry vehicle -- in essence the missile -- is going to work," he explained. "Also, the warhead is going to have to survive in a much more rugged environment, so that requires further testing too.

"I don't think they're there yet."

Miniaturization one of several key steps

Miniaturizing a nuclear weapon is one key part of building a nuclear-armed intercontinental ballistic missile.

The nuclear device also needs to be tough enough to be able to withstand the flight on a ballistic missile, experts say, and be housed in a "reentry vehicle" that can endure the intense heat generated by coming back into Earth's atmosphere.

In a February post for the North Korea watching blog 38 North , arms control expert Jeffrey Lewis said he thought North Korea was probably able to carry out each of those three steps.

But big questions remain about the reliability and accuracy of any weapon the North Koreans might be able to put together, wrote Lewis, who is the director of the East Asia Nonproliferation Program at the James Martin Center for Nonproliferation Studies.

Adding to concerns, North Korea claimed this month that it had successfully tested a submarine-launched ballistic missile . A South Korean defense official said, though, that the North was believed to still be years away from having a fully operational submarine missile system.

Nuclear progress likely to undermine regional stability

The apparent progress of the North Korean regime's nuclear weapons program is threatening to upend the United States' strategic calculations in the region.

"Pyongyang's advances in mobile ICBM capabilities could end up undermining the state of stable deterrence that currently exists on the Korean Peninsula," Victor Cha, Korea chair at the Center for Strategic and International Studies, wrote in an opinion article for CNN last month. "Put simply, these capabilities could give North Korea confidence that it is immune from any U.S. counterstrikes."

North Korea has demanded that the United States recognize it as a nuclear power. But the United States has said that North Korea's commitment to denuclearization is the starting point for any negotiations between the two sides.

North Korea is the subject of a raft of U.N. Security Council sanctions because of its nuclear tests and long-range rocket launches.

But the international measures don't appear to have stopped Pyongyang from continuing to develop its weapons programs, which it says it needs as a deterrent to the threat it perceives from the United States.

"I think we have rapidly approached the point of no return over the past five-years," Joel Wit, a visiting scholar at the U.S.-Korea Institute at Johns Hopkins University, said this month. "This program has gained a lot of momentum over the past few years, and not much has been done to stop it."