It prompted President Donald Trump to issue a warning of fire and fury on the North, while Pyongyang threatened to fire missiles towards the U.S. territory of Guam.
Witnesses in the Chinese city of Yanji, on the border with North Korea, said they felt a tremor that lasted roughly 10 seconds, followed by an aftershock.
South Korea is holding a National Security Council meeting to discuss the incident, presided by President Moon Jae-in, according to South Korea's presidential office.
The White House said Trump spoke with Abe regarding "ongoing efforts to maximize pressure on North Korea".
The head of the UN's nuclear watchdog, IAEA Director General Yukiya Amano said the nucleartest was "an extremely regrettable act" that was "in complete disregard of the repeated demands of the worldwide community".
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He continued: It's ridiculous that Trump was saying only a few days ago that there was restraint in North Korea... when there was really no indication of the sort.
"New Zealand will join the worldwide community in considering what further measures can be taken in response to this development". Pyongyang triggered a new rise in tensions in July, when it carried out two successful tests of an ICBM which apparently brought much of the U.S. mainland within range. "We will convene a National Security council meeting to gather and analyse the information", CNN quoted Abe as saying.
Seoul's weather agency and the Joint Chiefs of Staff said an artificial 5.7 magnitude quake occurred at 12:29 p.m. local time, in Kilju, northern Hamgyong province, the site where North Korea has conducted nuclear tests in the past.
But the state-run news agency reported that all components of the hydrogen bomb were 100-percent domestically-made and that Pyongyang can produce as many powerful nuclear weapons as it wants.
North Korea said on Sunday it has developed a more advanced nuclear weapon that has "great destructive power" as leader Kim Jong Un inspected a hydrogen bomb at the Nuclear Weapons Institute.
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The North says its missile development is part of a defensive effort to build a viable nuclear deterrent that can target U.S. cities.
The previous nuclear blast in North Korea is estimated by experts to have been around 10 kilotons. State-controlled media say it was a hydrogen bomb.
In hydrogen bombs, fusion - the merging of atoms - is used to unleash energy, whereas atomic bombs use nuclear fission, or the splitting of atoms.
Tensions on the Korean peninsula have been high since last month when North Korea threatened to launch missiles into the sea near the strategically located US Pacific territory of Guam after Trump said Pyongyang would face "fire and fury" if it threatened the United States.
Tensions between North Korea and the worldwide community flared last week, when Pyongyang flew a ballistic missile for the first time over Japan. South Korea's military said it has strengthened its monitoring and readiness while mulling a variety of possible responses that could be executed in collaboration with the U.S. This is an important component of the North's deterrent strategy: It feels it must showcase that it can do significant damage to a city on the USA mainland to change US calculus on military action or attempted regime change in North Korea.
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South Korea's military says North Korea is believed to have conducted its sixth nuclear test.