The council said in a statement Monday that it will begin work immediately on a new legally binding resolution addressing North Korea's violations.
The U.N.'s most powerful body held an emergency meeting at Japan's request after North Korea conducted its second nuclear test earlier Monday.
The council is demanding that North Korea abide by two previous resolutions, which among other things banned further nuclear tests and called for a return to six-party talks aimed at eliminating its nuclear program.
In Pyongyang early Monday, North Korea said that it had carried out a powerful underground nuclear test - much larger than one conducted in 2006. The regime also test-fired three short-range, ground-to-air missiles later Monday from the same northeastern site where it launched a rocket last month, the Yonhap news agency reported, citing unnamed sources.
The rocket liftoff, widely believed to be a cover for a test of its long-range missile technology, drew censure from the U.N. Security Council.
President Obama said Monday that's latest nuclear weapons and missile tests, "pose a grave threat".
"I strongly condemned the communist regime's reckless actions," Mr. Obama said in the White House Rose Garden. He added that North Korea would not find security or respect through threats and the pursuit of banned weapons. The president did not take questions.
In a statement earlier Monday morning Mr. Obama said the nuclear test should be "a matter of grave concern to all nations" and accused Pyongyang of behaving recklessly and defying international will.
Mr. Obama also said in the statement that the United States "will continue working with our allies and partners" in multilateral talks and will hold consultations with members of the U.N. Security Council on it and a subsequent series of test-firings of short-range ground-to-air missiles.
and Europe also condemned North Korea's reported nuclear test Monday as a violation of U.N. resolutions, while the U.S. and others threatened to take the isolated regime before the Security Council. Even joined the chorus of disapproval, saying it "resolutely opposed" the test.
The response from Beijing, the North's closest ally, came hours after most of the world had weighed in, but it was unequivocal.
"The Chinese government expresses that it is resolutely opposed to this," China's Foreign Ministry said in a statement. It wasn't clear if the delay was due to internal discussions or because the country's foreign minister is currently out of the country.
Reining in Pyongyang's nuclear program has been a continuing problem for U.S. administrations, dating to the Clinton administration. Former President George W. Bush labeled North Korea as a country that was part of an international "axis of evil," but the United States subsequently removed Pyongyang from its list of official state sponsors of terrorism when it shut down a nuclear installation late in the Bush administration.
The question now is just how great a threat does this new development signify and what are the options the Obama administration has for dealing with it.
Gen. James Cartwright, vice chairman of the Joint Chiefs of Staff, last month dismissed an earlier rocket launch as a failure- both technologically and as an effort to market its missiles to other countries.
"Would you buy from somebody that had failed three times in a row and never been successful?" he asked during a briefing at the Pentagon. Cartwright said the abortive missile launch showed that North Korea had failed to master the midair thrust shift from one rocket booster to another, an integral part of ballistic missile technology.
In his statement Monday, Mr. Obama noted that North Korea had "conducted a nuclear test in violation of international law."
"It appears to also have attempted a short range missile launch," the president said in his statement. "These actions, while not a surprise given its statements and actions to date, are a matter of grave concern to all nations. North Korea's attempts to develop nuclear weapons, as well as its ballistic missile program, constitute a threat to international peace and security."
"By acting in blatant defiance of the United Nations Security Council," he said, "North Korea is directly and recklessly challenging the international community. North Korea's behavior increases tensions and undermines stability in Northeast Asia."
"Such provocations will only serve to deepen North Korea's isolation. It will not find international acceptance unless it abandons its pursuit of weapons of mass destruction and their means of delivery."
Adm. Mike Mullen, chairman of the U.S. Joint Chiefs of Staff, said he believed the latest series of tests "just speak to the growing belligerence on the part of North Korea ... the growing defiance of international law."
Mullen told The Early Show co-anchor Harry Smith that "all of those things point to a country I think continues to destabilize that region and in the long term, should they continue to develop a nuclear weapons program, poses a grave threat to the United States."
Mullen, making appearances on the network morning news shows to pay tribute to troops on Memorial Day, told NBC's "Today" program that he was "very confident we can deal with a threat posed by North Korea."
"It's not just the U.S., but there are many other countries that are equally concerned," the admiral said. "This was not an unanticipated test on the part of North Korea, should we be able to confirm it. ... It's a country that continues to isolate itself, and the international community must continue to bring pressure to make sure they don't achieve a nuclear weapons program that can threaten other countries and the U.S. as well."
He did not discuss whether there were any changes in U.S. military alert status.
Wendy Sherman, a former Clinton administration adviser on North Korean policy, told The Associated Press: "We're sending the message that there is international law; there are international norms; that countries will be isolated from the international community."
"U.S. officials had expected that North Korea might conduct a second nuclear test," she said. "That said, this is as President Obama said, 'of grave concern.' "
Speaking on ABC's "Good Morning America," Mullen said: "We believe that North Korea continues to pursue a nuclear weapons program. A North Korea with nuclear weapons poses a great danger to its neighbors. They've also recently launched longer-range missiles pursuing literally ICBM kinds of missiles."
"In the long run," Mullen said, "a state like North Korea with nuclear weapons and the ability to fire those kind of missiles long range pose a threat to the United States."
CBS News foreign affairs analyst Pamela Falk notes the remarkably fast pace at which the relationship between Pyongyang and the Western world has soured since the highly visible destruction of the weapons-grade plutonium facility at Yongbyon last year.
That took place after President George W. Bush lifted U.S. sanctions under the Trading with the Enemy Act and began the actions necessary to take North Korea off the state sponsors of terrorism list. North Korea then destroyed its cooling tower - with U.S. media organizations there to watch - and the North Koreans turned over an inventory of some of their nuclear programs as part of the "six party talks".
Click here to read Falk's full analysis of the North's test and how it raises the stakes for Mr. Obama and America's allies.
But then things went south, reports Falk from United Nations headquarters. The North refused to verify the complete dismantling of its nuclear program, and the missile tests - and now the underground nuclear test - began. After the April 5th long-range missile launch, the U.N. Security Council issued a Presidential Statement, which drew quick and angry reaction from the North Korean regime.
Some analysts believe that a power struggle within North Korea is behind the seeming change of heart. There is talk that Jang Seong Taek, Kim Jung Il's brother-in-law, may be setting up a caretaker government in order to line up a succession for Kim Jung Il's youngest son, Kim Jong Un, if Kim Jung Il's health does not improve. Others believe it is to gain more concessions from the Obama administration.
North Korea earlier this year rejected a plan for additional U.S. food assistance and kicked out five groups distributing American aid in the country.
State Department spokesman Robert Wood said at the time, in mid-March, that the North gave no reason for refusing to accept U.S. food aid. But the rejection was worrisome to aid workers and U.S. officials.
North Korea faces chronic food shortages and has relied on outside aid to help feed its 23 million people since famine reportedly killed as many as 2 million in the 1990s, a result of natural disasters and mismanagement.
Japanese Prime Minister Taro Aso reacted sternly to the test, calling it a violation of U.N. sanctions.
"It is unacceptable," Aso said, adding that an emergency meeting of the Security Council expected later Monday in New York would deal with the test, North Korea's second. Japan is particularly sensitive to such actions because its territory is within North Korean missile range.
In Brussels, the European Union's foreign policy chief, Javier Solana, denounced the test as a flagrant violation of Security Council resolutions.
"These irresponsible acts by North Korea warrant a firm response by the international community," Solana said in a statement. "The European Union will be in contact with its partners to discuss appropriate measures."
French Foreign Ministry spokesman Eric Chevallier suggested the Security Council "will meet during the day today" to discuss the test and may talk about "the strengthening of sanctions."
"It (the claimed test) is a serious violation of the norm established by the Comprehensive Nuclear-Test-Ban Treaty and as such deserves universal condemnation," said Tibor Toth, executive secretary of the treaty's preparatory commission said in a statement.
Major nuclear powers have observed moratoriums on testing in recent years, but India, Pakistan and North Korea all have tested bombs since the treaty was negotiated in the 1990s. The U.S. has yet to ratify the treaty, although Mr. Obama has said he will push the Senate to do so.
North Korea has been under U.N. sanctions that bar it from nuclear and ballistic activity since its first atomic test in 2006.
A rocket launch in April - that the North said put a satellite into orbit but critics called a test of long-range missile technology - drew further condemnation from the world body.