President Trump suggested Sunday, after another underground nuclear test by North Korea, that he’ll halt trade with any country doing business with the rogue nation, as two members of the president's Cabinet issued tough warnings of their own.

“The United States is considering, in addition to other options, stopping all trade with any country doing business with North Korea,” tweeted Trump, in response to the regime of Kim Jong Un claiming to have detonated a hydrogen bomb underground.

Speaking to the media on Sunday, Defense Secretary Jim Mattis said that any threats by North Korea to the U.S. or its allies will be met with an "effective and overwhelming" military response.

"We are not looking to the total annihilation of a country, namely North Korea, but as I said, we have many options to do so," Mattis added.

Mattis' statement follows an announcement that the U.S., Japan, France, the U.K. and South Korea will meet on Monday morning for an emergency session of the United Nations Security Council.

Treasury Secretary Steve Mnuchin told "Fox News Sunday" earlier that he’s preparing a sanctions package that would cut off “all trade and other business,” with North Korea, following the country's overnight nuclear test, its sixth and most powerful.

“I will submit new sanctions for his strong consideration,” he said. “There’s much more we can do economically.”

Trump spoke with Japanese Prime Minister Shinzo Abe on Sunday, the White House said, adding that they “condemned North Korea's continued destabilizing and provocative actions, confirmed the two countries' ironclad mutual defense commitments, and pledged to continue close cooperation. President Trump reaffirmed the commitment of the United States to defending our homeland, territories, and allies using the full range of diplomatic, conventional, and nuclear capabilities at our disposal.”

Such a bomb is considered more powerful than any of the five nuclear ones North Korea has already tested. And it apparently triggered an artificial earthquake of at least a magnitude 5.7.

“I did speak with the president,” Mnuchin also said Sunday. “It’s clear this behavior is unacceptable. … I will draft a sanctions bill and send it to the president. We will work with our allies. We will work with China. But people need to cut off North Korea economically."

TRUMP CALLS NORTH KOREA 'DANGEROUS' AND 'GREAT THREAT' AFTER OVERNIGHT NUCLEAR TEST

The United States has already imposed economic sanctions on North Korea to stop the country’s pursuit on a nuclear weapon, including tests on inter-continental missiles on which to attach a nuclear warhead.

“The president has made clear he’ll consider everything. We’re not going to broadcast our action,” Mnuchin said in response to questions Sunday about whether Trump will curtail diplomatic and economic efforts and pursue military action.

Trump's tweet appears to be yet another attempt by him to get other countries, including North Korean trading partners like China, to try to stop the nuclear testing.

Other world leaders and the United Nations on Sunday also condemned North Korea’s actions.

Trump responded to the most recent bomb test with several tweets early Sunday in which he called North Korea’s actions “dangerous” and a “great threat.”

He also appears to show increasing frustration with South Korea for failing to get North Korea to stop the nuclear testing.

“South Korea is finding, as I have told them, that their talk of appeasement with North Korea will not work, they only understand one thing!” he tweeted.

Such tests in recent months have also sparked a war of words between Trump and North Korean leader Kim Jong Un that has created global concerns about either side taking military action in response.

Fox News' Kristin Brown, Nicole Darrah and Joseph Weber contributed to this report.