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"This act is profoundly destabilizing for regional security," Ki-Moon said, noting that, if true, it "seriously undermines" existing nuclear regulations.
He urged North Korea to "cease any further nuclear activities and meet its obligations for verifiable denuclearization."
The concern over North Korea's nuclear capability was renewed when a magnitude-5.1 earthquake was measured in the country near the site of an earlier nuclear weapons test, officials said Tuesday night. The tremblor was detected about 12 miles from Sungjibaegam and the South Korean weather agency said indications were that it was "artificial."
“We have perfectly succeeded in testing our first hydrogen bomb,” an anchor said on North Korean state TV. “It was one hundred percent capable from our own wisdom, technology and power. We have now scientifically test-proved a miniaturized hydrogen bomb.”
After the announcement, North Korea state TV replayed an earlier statement made in December, about leader Kim Jong Un’s plans to test a hydrogen bomb. New footage from the December statement shows what the North Koreans say is a photo of Kim Jong Un signing an authorization letter.
The Security Council is scheduled to hold a closed-door meeting to discuss the next steps.
The U.N.'s International Atomic Energy Agency released a statement noting that if confirmed, the test "is in clear violation of U.N. Security Council resolutions and is deeply regrettable."
John Kirby, a spokesman for the State Department, said in a statement, “We are aware of seismic activity on the Korean Peninsula in the vicinity of a known North Korean nuclear test site and have seen Pyongyang's claims of a nuclear test. We are monitoring and continuing to assess the situation in close coordination with our regional partners.
“While we cannot confirm these claims at this time, we condemn any violation of UN Security Council Resolutions and again call on North Korea to abide by its international obligations and commitments.”
North Korea conducted its first nuclear test in 2006 and only twice since, not including today's unconfirmed test, Kirby said.
"We condemn any violation of UN Security Council Resolutions and again call on North Korea to abide by its international obligations and commitments," he added.
The site of Tuesday's quake is about 5 miles from the Punggye-ri nuclear site where a test was conducted in 2013.
A quake measured at the site at that time registered the same magnitude. It was later deemed to be a nuclear explosion.
U.S. officials said that they will send up specially equipped "sniffer" planes to determine whether a nuclear test was conducted and, if so, what kind of test was done.
One official said the United States doesn't believe North Korea has the capability for a hydrogen bomb but can't be certain until testing is conducted.
ABC News' Luis Martinez, Tom Liddy and Emily Knapp contributed to this report.