The 15-member council was considering further sanctions against Pyongyang over the surprise nuclear test that UN chief Ban Ki-moon said was "deeply troubling" and "profoundly destabilizing for regional security."
The test drew swift condemnation from the international community, including from China, the North's main ally, and Washington, which said it was still studying the precise nature of the test and vowed to "respond appropriately."
North Korean state television said "the republic's first hydrogen bomb test" had been "successfully performed at 10:00 am (0130 GMT)."
"We have now joined the rank of advanced nuclear states," it said, adding that the test was of a miniaturized device.
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State television showed North Korean leader Kim Jong-Un's signed order -- dated December 15 -- to go ahead with the test, with a handwritten exhortation to begin 2016 with the "thrilling sound of the first hydrogen bomb explosion."
South Korean President Park Geun-Hye condemned what she described as a "grave provocation" and called for a strong international response.
The UN Security Council was meeting behind closed doors at the request of the United States and Japan, who were pushing for a new UN draft resolution on further sanctions.
"We will be working with others on a resolution on further sanctions," British Ambassador Matthew Rycroft told reporters.
The council was expected to issue a strong statement of condemnation, but any further measures hinged on the response from China, a veto-wielding council member.
Beijing has restrained US-led allies from stronger action against Pyongyang in the past, but has shown increasing frustration with the North's refusal to suspend testing.
The three previous tests in 2006, 2009 and 2013 triggered waves of UN sanctions.