With its detonation Tuesday of a “smaller and light” nuclear device, North Korea moved closer to its top technological goal of building an atomic weapon small enough to mount on a long-range missile, a capability that would turn the secretive police state from a regional menace into a global one.

Security analysts cautioned that there is no immediate way to verify the North’s assertion that it has succeeded in manufacturing a smaller — or miniaturized — warhead. They added that Pyongyang sometimes makes exaggerated claims.

Still, the latest nuclear test marks the clearest sign yet of the country’s intentions and signals a potentially contentious path in the months to come, as the North tries to test again and neighboring and Western countries try to dissuade it.

If the North wants to be fully confident that its nuclear devices work reliably, it will need to conduct subsequent tests — many of them, analysts say. Pyongyang hinted at such a path Tuesday, with its Foreign Ministry saying in a statement that the country was prepared to take unspecified “second and third stronger steps in succession” if the United States maintained its “hostile approach” toward the North.

That leaves officials in Washington, Seoul and Beijing scrambling to find a way to influence Pyongyang’s behavior — something they have not succeeded in doing.

Timeline: Highs and lows in the relationship between North and South Korea

The United States is limited in what it can do to change the North’s path, because the country is already so heavily sanctioned. In a statement Tuesday, Rep. Edward R. Royce (R-Calif.), chairman of the House Committee on Foreign Affairs, said President Obama should focus on “crippling the Kim regime’s military capabilities through stringent sanctions that tackle its illicit activities and cut off its flow of hard currency.”

But Washington, experts say, can do little beyond that without the cooperation of China, which is responsible for 70 percent of North Korea’s trade and which prefers the ruling Kim family to a united, and democratized, Korean Peninsula.

This time, China could react more harshly toward its traditional ally. Chinese leaders spent recent weeks trying strenuously to dissuade Pyongyang from the nuclear test, according to Western diplomats, who spoke on the condition of anonymity. Beijing’s inability to sway Pyongyang on the test points to growing exasperation in China with North Korean leader Kim Jong Eun and reflects a deteriorated relationship between the two countries that could have global consequences, the diplomats said.

The best indication of where North Korea and China stand will not be evident until the U.N. Security Council meets this week. Representatives of Western governments expressed hope Tuesday that Pyongyang’s open defiance of its powerful benefactor in Beijing would prompt China to support fresh penalties against the North’s leadership.

The test Tuesday was conducted in the face of strong opposition from the United States, and Obama said the North’s weapons program represented a “threat to U.S. national security and to international peace and security.”

This was the first test carried out under Kim Jong Eun, the young, third-generation North Korean leader who appears to favor the us-against-everybody militancy honed by his father and grandfather, with the United States characterized as the archenemy.

If North Korea is taken at its word, it now has a device — weighing less than 2,200 pounds — that is “missile-deliverable,” said Jeffrey Lewis, an East Asia nonproliferation expert at the Monterey Institute of International Studies.

“This does make them more of a threat,” Lewis said.

Still, said Siegfried Hecker, a scientist who has visited the North’s nuclear facilities several times, “such a weapon can only be used in a suicide attempt,” because any attack by Pyongyang would provoke a strong counterattack. “My opinion is, no, it’s not a game-changer,” Hecker said. “In the end, what it does, it makes the North Korean deterrent more credible.”

The North, for many reasons, is a global outlier in terms of nuclear testing. Among the eight countries to have tested a nuclear device, it is by far the most impoverished. It is the only country to detonate a nuclear weapon since 1998, amid a moratorium on testing by major states.

The North is also proving itself atypical in its race to build a small nuclear device before perfecting a larger, crude device, like the 12- to 20-kiloton “Little Boy” bomb that the United States dropped on Hiroshima toward the end of World War II. Most nuclear-armed countries have first built big nuclear warheads, then tried to shrink them. Some nuclear experts say that the North is trying to skip a step, going straight for the smaller device, although it is more difficult to build.

The detonation Tuesday had a yield of 6 to 7 kilotons, South Korea’s Defense Ministry said, compared with a 1-kiloton blast in 2006 and a blast that measured between 2 kilotons and 7 kilotons in 2009.

In its statement about the latest test, the North said it had used an “A-bomb . . . with great explosive power.” It also said that its deterrence had become “diversified” — a possible hint, experts said, that the nuclear device used highly enriched uranium, rather than the plutonium used in the first two tests. The North, though, did not go further in specifying its fissile material. Foreign countries could gather clues about what was used by monitoring radioactive emissions around the test site in coming days.

Such information could shed light on North Korea’s weapons program and whether its pile of fissile material is finite or growing. North Korea could still be working from its small pile of plutonium, though it froze its program in 2007. More likely, the country’s engineers are building bombs with uranium, which can be enriched to weapons-­grade levels in facilities that are tougher to detect by satellite.

Wan reported from Beijing. Colum Lynch at the United Nations and Yoonjung Soo in Seoul contributed to this report.