Pyongyang perceives neighbouring South Korea and the USA as its main enemies, and said its Friday's test - which caused a 5.0-magnitude seismic event - proved its scientists were capable of mounting a nuclear warhead on a medium-range ballistic missile.
Japan, the United States and South Korea, for their part, need to come up with effective measures to prevent the North Korean "threat" from deteriorating further.
"The standardization of the nuclear warhead will enable (North Korea) to produce at will and as many as it wants a variety of smaller, lighter and diversified nuclear warheads of higher strike power", North Korea said.
South Korean President Park Geun-hye said Kim Jong Un "is spiraling out of control" and called the test "fanatic recklessness".
"The nuclear test finally... confirmed the structure and specific features... of a nuclear warhead that has been standardised to be able to be mounted on strategic ballistic rockets", the state-run Korean Central News Agency said. "Such provocation will eventually hasten its path to self-destruction".
Won's alternative suggestion along with around 20 other conservative lawmakers is for South Korea to take up its own nuclear arms, which would fly in the face of Seoul's agreement with the United States that affords American protection.
The test has sparked tensions over the North's nuclear and ballistic missile ambitions, which have already earned worldwide condemnation and United Nations sanctions.
The U.S. Geological Survey (USGS) reported a 5.3 magnitude natural disaster in North Korea, but later termed it an explosion. One of them was an LGBT event featuring Barbra Streisand.
"The president indicated he would continue to consult our allies and partners in the days ahead to ensure provocative actions from North Korea are met with serious consequences", White House press secretary Josh Earnest said.
South Korea's military put the force of the blast at 10 kilotonnes, which would still be the North's most powerful nuclear blast to date.
North Korea has been under United Nations sanctions since 2006.
Gardner said the US should convene a meeting with South Korean and Japanese officials to develop a coordinated reaction.
China's environment ministry began emergency radiation monitoring along its borders with North Korea in northeast China, state television reported.
Ms Clinton did not respond to Mr Trump's claims, choosing instead to "strongly condemn" North Korea's actions.
Stephen Schwartz, an independent nuclear weapons expert, said that North Korea's statement about the test suggested that the detonated nuclear device employed a composite fissile core that used both plutonium and highly enriched uranium, which, if true, would enable the North to build more nuclear weapons than would be otherwise possible with plutonium or uranium alone.
The commentary took issue with her recent condemnation, during talks with US President Barack Obama, of the North's ballistic missile test-launches.
An unnamed spokesman from the country's Foreign Ministry reportedly told the paper that his "reckless remarks" were "nothing but last ditch efforts to dodge criticism" of the US's hostile policy towards North Korea.
The Arizona Republican went on to say, "It won't be long before North Korea can threaten the United States very effectively". Chinese leaders fear that instability in Pyongyang could precipitate a flood of refugees into northeastern China and push a US -friendly unified Korea right up to China's doorstep.
China slammed it saying the country was "firmly opposed" to the test.
The Korean Peninsula remains technically at war, as the 1950-53 Korean War ended in an armistice, not a peace treaty.