North Korea has tested three atomic bombs and is widely believed capable of firing a nuclear warhead. But in the eyes of the United States, North Korea most definitely is not a nuclear weapons state.

Experts believe that North Korea made military progress through its latest nuclear test on Tuesday. But for US policymakers, an even larger impact may be whether Pyongyang -- and other aspiring nuclear states -- benefit politically.

North Korea is seen as seeking recognition of its arsenal to ensure regime survival. North Korea, which declared itself a nuclear state in a constitution last year, said Tuesday that its nuclear "deterrent" was a "treasured sword."

Secretary of State John Kerry called for a strong international response to North Korea partially as a signal to Iran, which has pursued a nuclear program that some Western and Israeli officials fear is aimed at building a bomb.

"It is important for the world to have credibility with respect to our non-proliferation efforts," Kerry said, amid calls for even tighter sanctions against North Korea.

"And just as it is impermissible for North Korea to pursue this kind of reckless effort, so we have said it is impermissible with respect to Iran," Kerry told reporters on Wednesday.

But the clerical leadership of Iran, which insists that its nuclear program is for peaceful purposes, may draw the opposite lesson -- that North Korea, despite sweeping international sanctions, still has its bomb.

North Korea has alluded to learning lessons from Libya, where strongman Moamer Kadhafi gave up weapons of mass destruction in a bid to reconcile with the United States but was toppled in a Western-backed uprising in 2011.

The United States imposed sanctions in 1998 on India and Pakistan after the rivals' nuclear tests. But the United States effectively recognized India's program a decade later when, seeking warmer relations, it agreed to cooperate on civilian nuclear energy.

The United States has a more complicated relationship with Pakistan. But Washington turned to Islamabad to assist in the Afghanistan war and publicly promised not to seize its nuclear weapons, an emotive issue in Pakistan.

Experts said that the US refusal to recognize North Korea as a nuclear weapons state -- a decision that would have broad political and legal ramifications -- was not the same as denying the reality that it has the bomb.

"An analogy is a policeman who sees that a criminal in a hostage situation has a gun in his hand," said Bruce Klingner, a senior research fellow at the Heritage Foundation think tank.

"The policeman has to say, 'Yes, I see that he has a gun, I acknowledge that he has a weapon. But I don't accept the behavior and I don't abandon the rules,'" Klingner said.

North Korea said in 2003 that it was leaving the nuclear Non-Proliferation Treaty, although its actual withdrawal is a matter of dispute. India, Pakistan and Israel never signed the treaty.

Daryl Kimball, executive director of the Washington-based Arms Control Association, said that recognition of Pyongyang's program was a non-starter and that North Korea was in a far different situation than India or Pakistan.

Kimball said that despite the impasse on North Korea's nuclear status, the United States could eventually offer incentives such as food and energy aid and assurances of non-aggression in a bid to hold back the program.

"Those are small prices to pay for restraining what could be a much more capable nuclear missile arsenal years down the road," he said.

North Korea said it has miniaturized a nuclear device, a key step toward firing a nuclear weapon. The Institute for Science and International Security said that Pyongyang is likely already able to deploy a warhead on a missile that can strike Japan or South Korea.

China, the primary ally of North Korea, has also not recognized Pyongyang's nuclear arsenal. In its criticism of Tuesday's test, Beijing renewed its call for "denuclearization" of the Korean peninsula.

Experts believe that China does not want North Korea to enjoy the same nuclear weapons capabilities as Beijing or to scare US allies Japan and South Korea to the point that they consider their own nuclear weapons.