"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."
“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.”
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."
“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.