The measures, which Washington says are aimed at forcing Pyongyang to roll back its banned nuclear and weapons programmes, target more than 50 North Korea-linked shipping companies, vessels and trade businesses.
"Like we have said repeatedly, we consider any restrictions on us as an act of war," the North's foreign ministry said in a statement carried by the state-run KCNA news agency.
It also vowed a retaliation if the US "really has the nerves" to confront the North in a "rough" manner.
Trump warned on Friday that, if the latest sanctions don't work, the US would "go to phase two" that "may be a very rough thing", without elaborating.
"We already have our own nuclear weapon -- a treasured sword of justice to protect us from such threats from the US," the foreign ministry said.
The comment came hours before the North's senior delegation led by Kim Yong Chol, a blacklisted military general, is set to attend the closing ceremony of the South's Winter Olympics, which will also be attended by Trump's daughter Ivanka Trump.
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