If confirmed, it would be Pyongyang's fourth nuclear test since 2006 and mark a major upgrade in its capabilities.
But nuclear experts have questioned whether the size of the blast was large enough to have been from an H-bomb.
South Korea called the test a "grave provocation" but said it was difficult to believe it was from such a device.
China, North Korea's main ally, said it "firmly opposes" the test, saying it was carried out "irrespective of the international community's opposition".
Suspicions first emerged when an earthquake was registered near the Punggye-ri nuclear site in North Korea at 10:00 Pyongyang time (01:30 GMT), with the tremors rattling Chinese border cities.
Hours later, in a surprise announcement, a newsreader on North Korean state TV said: "The republic's first hydrogen bomb test has been successfully performed at 10:00 am on January 6, 2016."
Hydrogen bombs use fusion to create a blast far more powerful than a more basic atomic bomb, which use fission.
Bruce Bennett, an analyst with the Rand Corporation, was among those casting doubts: "The bang they should have gotten would have been ten times greater than what they're claiming.
"So Kim Jong-un is either lying, saying they did a hydrogen test when they didn't, they just used a little bit more efficient fission weapon - or the hydrogen part of the test really didn't work very well or the fission part didn't work very well."
Despite North Korea's claims, experts are sceptical that North Korea can make a nuclear weapon small enough to fit on a missile.
Observers agree a nuclear explosion of some kind took place and it seems to have been a bit bigger than the last test in 2013, but not nearly big enough to be a full thermonuclear explosion - an "H-bomb" - as Pyongyang claims.
North Korea has a determination to defy both world opinion and heavy sanctions to reach its nuclear goal. Crucially, its main ally, China, has proved either unwilling or unable to help.
International scepticism and condemnation have greeted North Korea's claim to have successfully carried out an underground hydrogen bomb test.