North Korea's issued new warnings over nuclear weapons - telling the U.S to expect "more gift packages".
The country's ambassador to the United Nations accused the U.S. of reckless provocations and attempts to put pressure on North Korea.
U.S. stocks have plummeted - with the S & P 500 experiencing its biggest single-day loss in three weeks.
Russian president Vladimir Putin condemned the latest nuclear test as "provocative".
However, at a news conference in China, Mr Putin stopped short of expressing support for more UN sanctions on North Korea, and said Russia viewed them as "useless and ineffective".
He also said it was "ridiculous" that the United States first slapped Russia with sanctions carried in the same bill that penalised North Korea, and "then asked us to help impose sanctions on North Korea".
North Korea's detonation of a hydrogen bomb on Sunday marked its most powerful nuclear test to date.
Mr Putin called for talks with North Korea, and warned against "military hysteria".
He said it was important that all parties, including North Korea, should not face "threats of annihilation" and "step on the path of cooperation".
The Russian leader added: "Whipping up military hysteria makes absolutely no sense in this situation.
"This is a road to nowhere."
Meanwhile, UN secretary-general Antonio Guterres warned the US and North Korea that "confrontational rhetoric may lead to unintended consequences" and stressed the nuclear crisis must be solved diplomatically.
Mr Guterres said it is "absolutely crucial" the UN Security Council is united in dealing with North Korea's nuclear and missile tests and that the US, Russia, China, Japan and South Korea use one strategy.
He told reporters at UN headquarters in New York on Tuesday that North Korea's nuclear and missile tests threaten regional and international stability.
He accused North Korea's leaders of "needlessly and recklessly (putting) millions of people at risk including its own citizens already suffering drought, hunger and serious violations of their human rights".
Mr Guterres offered to support any efforts to peacefully resolve "this alarming situation".