"President Trump and President Moon pledged to continue to apply strong diplomatic and economic pressure on North Korea and to make all necessary preparations to deter and defend against the growing threat posed by North Korea", read a White House statement.
The North has previously claimed to have successfully tested an H-bomb, after its fourth blast in January a year ago, but experts doubted the claim at the time, due to the relatively weak yield. China said it had detected a second, 4.6 magnitude quake with near identical coordinates eight minutes later.
Secretary of State Rex W. Tillerson has previously suggested that the United States would be open to talks with North Korea if it ceased its missile tests and met other conditions.
In a series of tweets, Trump said that North Korea continued to be "very hostile and dangerous" towards the United States.
With his previous threat to rain "fire and fury" on North Korea and warning that the United States military is "locked and loaded" to respond to Kim Jong Un's provocations, Trump set up a test of wills with his unpredictable adversary. "They [North Korea] only understand one thing!" said Trump.
Trump was hardly alone as leaders around the world condemned the nuclear test.
The broadcaster carried images of leader Kim Jong-un, the third generation of the family to rule the Democratic People's Republic of Korea, as the country is officially known, sitting at a circular table with a general and three other officials. But he also said he was "skeptical that this design has been miniaturized to fit reliably on a ballistic missile". The President and his national security team will have a meeting to discuss further later today. Officials in Seoul said Trump's national security adviser, H.R. McMaster, spoke with his South Korean counterpart for 20 minutes about an hour after the detonation.
Nuclear tests are crucial to perfecting sophisticated technologies and to demonstrating to the world that claims of nuclear prowess are not merely a bluff.
North Korea's hydrogen bomb test setoff off a manmade natural disaster near the test site. That could be hard to independently confirm.
"This is now even more pressing".
At the same time, the simple power of the blast was convincing. Japan's Defense Minister Itsunori Onodera said it might have been as powerful as 70 kilotons.
Juche is North Korea's homegrown ideology of self-reliance that is a mix of Marxism and extreme nationalism preached by state founder Kim Il Sung, the current leader's grandfather. "More tests now will be meaningless", Koo Kab-Woo of the University of North Korean Studies told AFP.
Trump warned last month that the U.S. military was "locked and loaded, should North Korea act unwisely" and that the USA would unleash "fire and fury" on the North if it continued to threaten America.
Pyongyang has defied United Nations sanctions to develop nuclear weapons and to test missiles which could potentially reach the mainland US.
Peskov also said that Putin was aware of a US decision to take over Russian diplomatic property in the United States.
"I don't think that it's been helpful", Castro said.
Mr Albright, however, still questioned the North's claim that it was a genuine two-stage thermonuclear device. Norsar, a Norwegian natural disaster monitoring agency, estimated the yield at 120 kilotons, significantly above the 15 kiloton "Little Boy" bomb dropped on Hiroshima and the 20 kiloton "Fat Man" dropped on Nagasaki at the end of the Second World War.