The measures, which Washington says are aimed at forcing Pyongyang to roll back its banned nuclear and weapons programs, 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.
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.
In response, the North also vowed to "subdue the US in our own way" if provoked, saying "Trump is trying to change us with such sanctions and hostile remarks, which shows his ignorance about us".
"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.
China also reacted angrily to the new US measures, saying on Saturday the unilateral targeting of Chinese firms and people risked harming cooperation on North Korea.
Hours later, Senior North Korean officials visiting South Korea on Sunday said Pyongyang was open to talks with Washington.
The visiting delegation, led by former military intelligence chief Kim Yong Chol, also said developments in relations between the two Koreas and between North Korea and the United States should go hand in hand, the South’s presidency said in a statement.
Kim Yong Chol said North Korean leader Kim Jong-un wanted to improve ties with Washington and had "ample intentions of holding talks" with its rival.
AFP, Reuters and AP contributed to this story.