Treasury Secretary Steve Mnuchin said Sunday that he's preparing a sanctions package against North Korea that would cut off "all trade and other business", with the rogue nation following its overnight nuclear test, its sixth and most powerful.
The latest test appeared to mark a significant step forward in North Korean leader Kim Jong Un's quest for a nuclear missile capable of striking anywhere in the United States.
Despite the US' strong stance, UK Foreign Minister Boris Johnson has advised caution with military action.
Other world leaders and the United Nations on Sunday also condemned North Korea's actions.
"The fact that North Korea forced through a nuclear test this time is absolutely unacceptable to our country", Abe said in a statement.
He said the United States is "not looking to the total annihilation" of North Korea.
When asked by a reporter during a church visit if he would attack the North Mr Trump said: "We'll see".
Such a move would have serious ramifications, resulting in a halt to U.S. trade with China, who remains its key economic partner.
North Korea's state-run Korean Central News Agency warned on Sunday, "If the US imperialists awkwardly provoke the DPRK, they would not be able to escape from the greatest disaster". China is a large trading partner of North Korea, but it is also the largest US trading partner in terms of goods imported and exported.
North Korean state television was nearly jubilant in announcing what the regime calls a successful test of a hydrogen bomb.
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If North Korea hasn't already developed a hydrogen bomb then it is likely it will, before long, unless dramatically stopped.
Mr Mattis was speaking after Pyongyang announced that it had successfully tested a hydrogen bomb that could be loaded on to a long-range missile.
"We strongly urge the DPRK (North Korea) to face the strong will of denuclearization from the global community, earnestly abide by the relevant resolutions of the UN Security Council, stop taking mistaken actions which worsen the situation and are also not in line with its own interests, and effectively return to the track of solving the problem through dialogue", it added.
North Korea has previously conducted nuclear tests in 2006, 2009, 2013, and two in 2016, with explosive yields of less than one kiloton, 2-4 kilotons, 6-9 kilotons, 7-10 kilotons, and 20-30 kilotons, respectively. But he summed up North Korea's rapid progress with a dire warning.
"We always have military options, but they're very ugly", said Mark Hertling, a retired US Army general and CNN military analyst.
The statement questioned the growing worldwide call for more sanctions, noting that sanctions so far had "not led to any positive outcome".
Moon "will never allow North Korea to continue advancing its nuclear and missile technologies", said Moon's national security adviser, Chung Eui-yong.
She expects members of congress to receive another briefing on the Korea situation as soon as this week.