By Jack Kim

SEOUL (Reuters) - South Korea said on Saturday that North Korea's nuclear capability is expanding fast, echoing alarm around the world over the isolated state's fifth and biggest nuclear test, carried out in defiance of U.N. sanctions.

North Korea conducted the test on Friday and said it had mastered the ability to mount a warhead on a ballistic missile, ratcheting up a threat that rivals and the United Nations have been powerless to contain.

The test showed North Korean leader Kim Jong Un was unwilling to alter course, and that tougher sanctions and pressure were needed to apply "unbearable pain on the North to leave no choice but to change", South Korean Foreign Minister Yun Byung-se said.

"North Korea's nuclear capability is growing and speeding to a considerable level, considering the fifth nuclear test was the strongest in scale and the interval has quickened substantially," Yun told a ministry meeting convened to discuss the test.

The blast, on the 68th anniversary of North Korea's founding, drew global condemnation.

The United States said it would work with partners to impose new sanctions, and called on China to use its influence - as North Korea's main ally - to pressure Pyongyang to end its nuclear program.

In Beijing on Saturday, Chinese Vice Foreign Minister Zhang Yesui told North Korea's ambassador to China, Ji Jae Ryong, that the test was "not conducive to the peace and stability of the Korean peninsula", China's Foreign Ministry said.

"China urges North Korea not to take any more actions that could exacerbate tensions, and return as soon as possible to the correct direction of denuclearisation," Zhang said.

But Russia was skeptical that more sanctions were the answer, while China was silent on the prospect of a new U.N. Security Council resolution, although state media did carry commentaries criticizing the North.

Under 32-year-old leader Kim, North Korea has sped up development of its nuclear and missile programs, despite U.N. sanctions that were tightened in March and have further isolated the impoverished country.

DENUNCIATION

The Security Council denounced North Korea's decision to carry out the test and said it would begin work immediately on a resolution. The United States, Britain and France pushed for the 15-member body to impose new sanctions.

U.S. President Barack Obama said after speaking by telephone with South Korean President Park Geun-hye and with Japanese Prime Minister Shinzo Abe on Friday that they had agreed to work with the Security Council and other powers to vigorously enforce existing measures and to take "additional significant steps, including new sanctions".

Russian Foreign Minister Sergei Lavrov said it may take more than additional sanctions to resolve the crisis, suggesting that a Security Council agreement may prove difficult.

"It is too early to bury the six-party talks. We should look for ways that would allow us to resume them," Lavrov said.

The talks, aimed at ending the North's nuclear program, involve the United States, Russia, Japan, South Korea, China, and North Korea, but have been defunct since 2008.

U.S. Secretary of State John Kerry said the United States had repeatedly offered talks to North Korea, but Pyongyang had to accept de-nuclearization, which it had refused to do.

"We have made overture after overture to the dictator of North Korea," he said, adding that he ultimately hoped for an outcome similar to that reached in nuclear talks with Iran.

China said it was resolutely opposed to the test but Foreign Ministry spokeswoman Hua Chunying would not be drawn on whether China would support tougher sanctions.

On Saturday, the Chinese state-run tabloid the Global Times said North Korea was wrong in thinking that building nuclear weapons would provide it with more security or prestige.

"Owning nuclear weapons won't ensure North Korea's political security," it said in an editorial. "On the contrary, it is poison that is slowly suffocating the country."

"OUT OF CONTROL"

South Korea's Park said late on Friday that Kim was "mentally out of control", blind to all warnings from the world and neighbors as he sought to maintain power. "The patience of the international community has come to the limit," she said.

North Korea, which calls the South and the United States its main enemies, said its "scientists and technicians carried out a nuclear explosion test for the judgment of the power of a nuclear warhead", according to its official KCNA news agency.

It said the test proved North Korea was capable of mounting a nuclear warhead on a medium-range ballistic missile, which it last tested on Monday when Obama and other world leaders were gathered in China for a G20 summit.

Pyongyang's claims of being able to miniaturize a nuclear warhead have never been independently verified.

Its continued testing in defiance of sanctions presents a challenge to Obama in the final months of his presidency and could become a factor in the U.S. presidential election in November, and a headache to be inherited by whoever wins.

North Korea has been testing different types of missiles at an unprecedented rate this year, and the capability to mount a nuclear warhead would be especially worrisome for its neighbors South Korea and Japan.

The Pentagon does not have evidence that North Korea had been able to miniaturize a nuclear weapon, Pentagon spokesman Gary Ross said. But he added: "Given the consequences of getting it wrong, it is prudent for a military planner to plan for the worst."

Jeffrey Lewis of the California-based Middlebury Institute of International Studies said the highest estimates of seismic magnitude suggested this was North Korea's most powerful nuclear test so far, at yield of 20 to 30 kilotonnes.

That would make this test larger than the nuclear bomb dropped by the United States on the Japanese city of Hiroshima in World War Two, which had an output of about 15 kilotonnes.

South Korea's military put the force of the blast at 10 kilotonnes, which would still be the North's most powerful blast to date.

"The important thing is that, five tests in, they now have a lot of nuclear test experience. They aren't a backward state any more," Lewis said.

(Additional reporting by Ju-min Park in Seoul, Ben Blanchard in Beijing, Michelle Nichols at the United Nations, Phil Stewart in Oslo, David Brunnstrom in Geneva; Editing by Mike Collett-White and Kevin Liffey)