Treasury Secretary Steven Mnuchin promised to consider a sanctions package that may cut off "all trade and all other business" with North Korea's trading partners after North Korea's latest nuclear test, saying the rogue country's behavior is "unacceptable."

"We are going to strongly consider everything at this point and, again, I will draft a package for [President Trump's] strong consideration that would go as far as cutting off all trade and other business," Mnuchin said in response to whether a package would also censure Chinese financial institutions and companies on "Fox News Sunday."

"This behavior is unacceptable, and if countries want to do business with the United States, they obviously will be working with our allies and others to cut off North Korea economically."

President Trump later backed up Mnuchin's statement in a tweet.

"The United States is considering, in addition to other options, stopping all trade with any country doing business with North Korea," he said.

Mnuchin would not say whether this was the tipping point the president was referring to when considering taking military options to demilitarize the Korean Peninsula.

Chinese media have reported the North Korea nuclear missile test was not an atomic bomb, but a much more powerful hydrogen bomb.

Mnuchin would not confirm whether the U.S. intelligence community was aware North Korea was capable of miniaturizing such a weapon to put on a nuclear warhead.

"Chris, I can only say that our intelligence community has been doing an amazing job on this and on other issues," Mnuchin said to host Chris Wallace.

Mnuchin also confirmed the Trump administration was considering renegotiating its trade deal with South Korea, but would not comment on whether the timing of trade talks would complicate security discussions.

"In the case of South Korea, we obviously provide a lot of military assistance and others in what we are doing to protect them and the president has made it clear that we want a better economic deal," Mnuchin said.

"But there's been no decisions made other than renegotiating that trade agreement at this point."