South Korea has conducted a missile drill simulating an attack on the North Korean nuclear site, in response to Pyongyang's sixth test. The live-fire exercise saw rockets launched from fighter jets and ballistic missiles from the ground.
It came as the US warned that any threat to itself or its allies would be met with a "massive military response".
The North says it tested a hydrogen bomb that can fit on a long-range missile.
Pyongyang has repeatedly defied UN sanctions and international pressure by developing nuclear weapons and testing missiles, and the provocations have only intensified.
In the past two months it has conducted intercontinental ballistic missile tests, sending one over mainland Japan into the Pacific Ocean. It has also threatened to fire missiles towards the US Pacific territory of Guam.
The UN Security Council is to hold an emergency meeting later on Monday to discuss its response.
Ahead of that meeting, South Korea and Japan's leaders agreed to push for a stronger UN resolution on North Korea, said a South Korean presidential palace spokesman.
The Security Council last imposed sanctions in August, targeting North Korean exports.
What is the significance of the drills?
The BBC's Robin Brant in Seoul says the drill was designed to show the country moving to a high state of alert. It tested conventional weapons - the country does not have nuclear capability.
But South Korea's military said on Monday that the simulated target was "set in consideration of" Punggye-ri, the site where North Korea carried out its test.
"The training demonstrates the South Korean military's resolve to destroy not only the origin of provocation but also the enemy's leadership and supporting forces if they threaten the security of our people," Col Roh Jae-cheon, the army spokesman is quoted by South Korea's Yonhap news agency.
South Korea and the US also agreed "in principle" to revise current guidelines so that the South can double the maximum payload of its ballistic missiles, Yonhap also reported.
How did the nuclear test unfold?
On Sunday seismologists started picking up readings of an earth tremor in the area where North Korea has conducted nuclear tests before.
The US Geological Survey put the tremor at 6.3 magnitude.
North Korean state media later confirmed it was no earthquake, claiming it was in fact its sixth and most powerful nuclear test, detonating a hydrogen bomb that could be loaded onto a long-range missile.
Pyongyang then released pictures of leader Kim Jong-un with what state media said was a new type of hydrogen bomb.
Officials in China, where the blast was felt as a tremor, said they were carrying out emergency radiation testing along the border with North Korea.
Although experts have urged caution, Sunday's event appears to be the biggest and most successful nuclear test by North Korea to date - and the messaging is clear. North Korea wants to demonstrate it knows what makes a credible nuclear warhead.
More on the way
BBC's Robin Brant in Seoul
It's become a war of photographs, for a few hours at least. After Sunday's underground nuclear test in the North, the government in the South released images of its own missiles launched at dawn.
It's the second time in a week that Seoul has responded with a test bombing run. That's in addition to the show of military might that was on display in its annual exercise with US forces at the end of last month.
That enraged Pyongyang, as it does every year, and there's more missiles on the way. South Korea is expected to approve the deployment of the US missile defence system known as Thaad (Terminal High-Altitude Area Defense) - an environmental impact report is the final hurdle.
But that involves a fourth party. China has criticised the system, claiming it threatens its security.
What has the reaction been?
The nuclear test prompted an angry response from US President Donald Trump who denounced the test as "hostile" and "dangerous", and called the North a "rogue nation".
He added that the US was considering stopping all trade with any country doing business with North Korea, which relies on China for about 90% of its foreign trade.
Meanwhile US Defence Secretary James Mattis later told reporters that while the US would respond to any threat "with a massive military response, a response both effective and overwhelming", they were "not looking to the total annihilation of a country, namely North Korea".
A White House statement also said that Washington would defend itself and its allies "using the full range of diplomatic, conventional, and nuclear capabilities at our disposal".
South Korean President Moon Jae-in called the test an "absurd strategic mistake" and urged for the "strongest possible" response, including new UN Security Council sanctions to "completely isolate" the country.
China, meanwhile, also expressed "strong condemnation" and said the state "had ignored the international community's widespread opposition".
What does the test tell us?
South Korean officials said the latest test took place at Punggye-ri nuclear test site in Kilju County.
The "artificial quake" was 9.8 times more powerful than the tremor from the North's fifth test in September 2016, the state weather agency said.
Hydrogen bombs are many times more powerful than an atomic bomb. They use fusion - the merging of atoms - to unleash huge amounts of energy, whereas atomic bombs use nuclear fission, or the splitting of atoms.
Analysts say the North's claims should be treated with caution, but that its nuclear capability is clearly advancing.
North Korea's nuclear tests