Although it claimed that a nuclear test in January previous year was of a hydrogen bomb, experts said the seismic waves generated were consistent with an ordinary nuclear device, not a thermonuclear one.
The ministry said in a statement on its website that China resolutely opposed and strongly condemned North Korea's actions, and urged the country to respect UN Security Council resolutions.
Under third-generation leader Kim, North Korea has been pursuing a nuclear device small and light enough to fit on a long-range ballistic missile, without affecting its range and making it capable of surviving re-entry. State-controlled media say it was a hydrogen bomb.
South Korea's Yonhap news reported the South Korean army's Joint Chief of Staff's statement that a man-made 5.6 magnitude natural disaster was detected in Punggye-ri, North Korea.
During a visit to the country's Nuclear Weapons Institute, North Korean leader Kim Jong Un "watched an H-bomb to be loaded into new ICBM [intercontinental ballistic missile]", KCNA reported.
Japan also raised the prospect of further sanctions, saying curbs on North Korea's oil trade would be on the table.
Japan's meteorological agency said the resulting tremors were at least 10 times as powerful as North Korea's previous nuclear test, last September. The last nuclear test Pyongyang conducted, which was almost a year ago, triggered a 5.3-magnitude seismological event.
The Earthquake Administration said in a statement on its website that the quake, which occurred around 3:30 GMT, was recorded at a depth of zero kilometres.
North Korea's state-run television broadcast a special bulletin Sunday afternoon to announce the test. That would be 3:30 p.m.in Seoul and Tokyo, and 2:30 a.m. EDT.
On Sunday, North Korean leader Kim Jong Un reportedly inspected a "super explosive" hydrogen bomb for its intercontinental ballistic missiles. What appeared to be the nose cone of a missile could also be seen near the alleged bomb in one picture, which could not be independently verified and was taken without outside journalists present.
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 US. That was revised up from an initial report of 5.6.
Kim Kardashian once called herself Taylor Swift's 'biggest fan' years before feud
It all began when she was asked the number one song on her iPod (yes, those still existed). West used a floating stage on his recent Saint Pablo Tour.
South Korea's weather agency estimated the nuclear blast yield of the presumed test was between 50 and 60 kilotons, or five to six times stronger than North Korea's fifth test in September 2016.
South Korea's presidential office said the security chiefs for Seoul and Washington had spoken following North Korea's sixth nuclear test.
The first, more powerful quake measured magnitude 6.3 and was 10km deep, according to the US Geological Survey said, again suggesting a nuclear device.
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, KCNA news agency said.
Impoverished North Korea and the rich, democratic South are technically still at war because their 1950-53 conflict ended in a truce, not a peace treaty.
The developments are raising already high tensions on the Korean Peninsula and in Washington that the North is getting closer to its goal of an arsenal of intercontinental ballistic missiles (ICBMs) that can reach the USA mainland.
In 2015, the allies completed the drawing of a new operational plan, OPCON 5015, which calls for a pre-emptive strike on the North's nuclear and missile facilities as well as "decapitation" raids targeting its leadership. But if the North Korean program is advancing at the pace it claims, it may be too late to debate over negotiations or their meaning - the North may be closer than anyone expected to having a viable nuclear deterrent.
The White House said President Donald Trump spoke with Prime Minister Shinzo Abe of Japan regarding "ongoing efforts to maximize pressure on North Korea".
Earlier, the party's newspaper published photos of Kim examining what it said was a nuclear warhead being fitted onto an intercontinental ballistic missile.
Sunday's statement by the state-run Korean Central News Agency will raise already high worries on the Korean Peninsula and in Washington that the North is closer to its goal of an arsenal of viable nuclear ICBMs that can reach the USA mainland. "President Trump noted that he looks forward to continued trilateral coordination on the margins of the United Nations General Assembly".