The first involved what it claims to have been a hydrogen bomb and the second was its most powerful ever.
Analysts have warned other nations to treat the matter seriously, adding that the regime's nuclear programmes are picking up speed.
U.S. monitors measured a 6.3-magnitude tremor near the North's main testing site site at Punggye-ri.
North Korean leader Kim Jong-un inspected the loading of an "H-bomb into the ICBM during his visit to the Nuclear Weapons Institute, according to the Korean Central News Agency (KCNA)".
Jean-Yves Le Drian called the situation following a string of missile tests by Pyongyang "extremely serious" and urged the reclusive state to turn to dialogue to ease spiralling tensions. "Since the KMA's announcement, we've been telling people that it's because of a quake in the North".
A series of recent missile tests has caused growing worldwide unease.
This would make it the North's most powerful nuclear test to date. There is also scepticism about the North's claims to have developed a hydrogen bomb.
North Korea is thought to have a handful of rudimentary nuclear bombs and has spent decades trying to ideal a multistage, long-range missile to eventually carry smaller versions of those bombs.
Nuclear weapons expert Catherine Dill told the BBC it was not yet clear exactly what nuclear weapon design was tested.
Current information did not definitively indicate that a thermonuclear weapon had been tested "but it appears to be a likely possibility at this point", she said.
KCNA said the hydrogen bomb's power is adjustable to hundreds of kilotons and can be detonated at high altitudes, with its indigenously produced components allowing the country to build as many nuclear weapons as it wants.
What has the reaction been?
O'Carroll said that he expects North Korea to launch a new ICBM test soon, with a long-range trajectory of thousands of kilometers into the Pacific Ocean.
"I sincerely hope that this will serve as the final wake-up call to the worldwide community to outlaw all nuclear testing by bringing the CTBT into force", Mr Zerbo said.
Pyongyang's only major ally, China, said it strongly condemned the detonation.
Despite being North Korea's most important worldwide ally, a Chinese foreign ministry statement said North Korea "has ignored the global community's widespread opposition, again carrying out a nuclear test".
How can the world respond?
"There is possibility that North Korea carried out a nuclear test today".
How did news of the test emerge?
Officials in Seoul put the magnitude at 5.7 while the US Geological Survey said it was a magnitude 6.3.
This bomb test came just hours after Japanese Prime Minister Shinzo Abe spoke to President Trump about escalating the response to North Korea's acts of aggression.
The quake was felt in northern China, with emergency sirens blaring in Yanji, near the North Korean border, according to local media.