Story highlights Obama: The danger posed by North Korea warrants further action by the world

The Chinese government says it "resolutely opposes" the nuclear test

Russia condemns North Korea's actions but admonishes its adversaries

Office of Ban Ki-moon: The U.N. secretary-general is "gravely concerned"

Reaction to North Korea's nuclear test -- its third since 2006 -- poured in Tuesday from around the world:

Barack Obama, U.S. president:

"This is a highly provocative act that ... undermines regional stability, violates North Korea's obligations under numerous United Nations Security Council resolutions, contravenes its commitments under the September 19, 2005, Joint Statement of the Six-Party Talks, and increases the risk of proliferation.

North Korea's nuclear weapons and ballistic missile programs constitute a threat to U.S. national security and to international peace and security. The United States remains vigilant in the face of North Korean provocations and steadfast in our defense commitments to allies in the region."

"The danger posed by North Korea's threatening activities warrants further swift and credible action by the international community. The United States will also continue to take steps necessary to defend ourselves and our allies."

Photos: Fear, concern after North Korea nuclear test Photos: Fear, concern after North Korea nuclear test Fear, concern after North Korea nuclear test – People watch a television broadcast reporting the North Korea's nuclear test at the Seoul Railway station on February 12, 2013 in Seoul, South Korea. Hide Caption 1 of 7 Photos: Fear, concern after North Korea nuclear test A North Korean soldier rides a bike beside a river crossing on the Yalu River near the North Korean town of Sinuiju on February 12, 2013. Hide Caption 2 of 7 Photos: Fear, concern after North Korea nuclear test Fear, concern after North Korea nuclear test – South Korean conservative protesters position a defaced North Korean flag as they participate in a rally demonstrating against North Korea's nuclear test on February 12, 2013 in Seoul, South Korea. Hide Caption 3 of 7 Photos: Fear, concern after North Korea nuclear test Fear, concern after North Korea nuclear test – Japanese Prime Minister Shinzo Abe leaves his official residence after he attended the security council meeting in Tokyo on February 12, 2013. Hide Caption 4 of 7 Photos: Fear, concern after North Korea nuclear test Fear, concern after North Korea nuclear test – An official of the Korea Meteorological Administration shows a seismic image of a tremor caused by North Korea's nuclear test. Hide Caption 5 of 7 Photos: Fear, concern after North Korea nuclear test Fear, concern after North Korea nuclear test – A North Korean soldier patrols along the Yalu River near the North Korean town of Sinuiju on February 12, 2013. Hide Caption 6 of 7 Photos: Fear, concern after North Korea nuclear test Fear, concern after North Korea nuclear test – North Korea said Tuesday that it had conducted a new, more powerful underground nuclear test using more sophisticated technology. Hide Caption 7 of 7

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U.S. Defense Secretary Leon Panetta

"We're going to have to continue to deal with rogue states like Iran and North Korea. We just saw what North Korea's done in these last few weeks -- a missile test and now a nuclear test. They represent a serious threat to the United States of America and we've got to be prepared to deal with that."

China's Ministry of Foreign Affairs:

The Chinese government "resolutely opposes" North Korea's nuclear test, the Ministry of Foreign Affairs said in a prepared statement.

"Holding up peace and stability in Northeast Asia is China's resolute position," it said. "We strongly urge (North Korea) to abide by (its) promise to denuclearize and take no further action that will worsen the situation."

Park Geun-hye, South Korean president-elect:

"Despite the strong warning from the international community and South Korea, North Korea has conducted its third nuclear test, and we strongly condemn it."

"The North Korean nuclear test is a serious threat to the peace of the Korean peninsula and the world, and it has hampered the credibility between the South and North."

Russia's Ministry of Foreign Affairs:

The Russian Federation condemned the test of the nuclear explosive but also called on other nations not to react with a show of military might.

In a written statement, the foreign ministry said North Korea's actions are an affront to the community of nations. "It's doubly sad that we are talking about the state with which our country has a long history of good neighborliness," the ministry said.

Russia called upon North Korea to stay away from a nuclear missile program, adhere to U.N. Security Council regulations and return to six-party talks.

Then the foreign ministry directed a message to North Korea's adversaries: "We expect that the current action of Pyongyang will not be used as an excuse to increase military activities around the Korean Peninsula."

Shinzo Abe, Japanese prime minister:

"North Korea's nuclear testing is a grave threat to the safety of Japan and a serious challenge against international disarmament framework based on the non-nuclear proliferation treaty. We can never tolerate it as it significantly compromise the peace and safety of Northeast Asia and the international society."

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"Japan firmly protests and sternly condemns the nuclear testing."

Statement from the office of Ban Ki-moon, U.N. secretary-general:

"The Secretary-General condemns the underground nuclear weapon test conducted by the Democratic People's Republic of Korea (DPRK) today. It is a clear and grave violation of the relevant Security Council resolutions.

It is deplorable that Pyongyang defied the strong and unequivocal call from the international community to refrain from any further provocative measures. The Secretary-General had repeatedly called on the new leadership in Pyongyang to address international concerns and start building confidence with neighboring countries and the international community.

The Secretary-General is gravely concerned about the negative impact of this deeply destabilizing act on regional stability as well as the global efforts for nuclear non-proliferation. He once again urges the DPRK to reverse course and work toward de-nuclearization of the Korean peninsula.

The Secretary-General is confident that the Security Council will remain united and take appropriate action. In the meantime, the Secretary-General remains in close contact with all concerned parties and stands ready to assist their efforts."

Yukiya Amano, International Atomic Energy Agency director general:

"This is deeply regrettable and is in clear violation of U.N. Security Council resolutions."

"The IAEA remains ready to contribute to the peaceful resolution of the DPRK nuclear issue by resuming its nuclear verification activities in the country as soon as the political agreement is reached among countries concerned."

Statement from NATO:

"We condemn in the strongest terms the test by North Korea of a nuclear weapon, conducted in flagrant violation of relevant United Nations Security Council resolutions.

This irresponsible act, along with the December missile launch, poses a grave threat to international and regional peace, security and stability. North Korea's pursuit of weapons of mass destruction represents continued defiance of the U.N. Security Council and the broader international community."

William Hague, British foreign secretary:

"I strongly condemn this development, which is a violation of U.N. Security Council Resolutions 1718, 1874 and 2087. North Korea's development of its nuclear and ballistic missile capabilities poses a threat to international and regional security. Its repeated provocations only serve to increase regional tension, and hinder the prospects for lasting peace on the Korean Peninsula."

Francois Hollande, French president:

"I condemn in the strongest terms the nuclear test just made by North Korea," Hollande said on the French government's website.

"France again urges North Korea to immediately comply with its international obligations and to carry out complete, verifiable and irreversible dismantling of its nuclear and missile programs."

Statement from the German Foreign Office:

Foreign Minister Guido Westerwelle "strongly condemns" North Korea's nuclear test. The "international community should consider further sanctions against the regime," the agency's official Twitter feed said.

Bob Carr, Australian foreign affairs minister:

"The Australian government condemns in the strongest possible terms nuclear testing by North Korea.

"Nuclear testing by North Korea clearly violates United Nations Security Council resolutions ... which demand North Korea not conduct any further nuclear tests.

"North Korea's development of nuclear weapons and missiles and its proliferation of sensitive technologies threaten international peace and security."