Legal challengeswere mounting to Mr Trump's proposed ban on people from six predominantly Muslim countries entering the US.
Bob Ferguson, the Attorney General of Washington state, said he would ask Judge James Robart in Seattle to block it.
Judge Robart issued a nationwide restraining order halting Mr Trump's original, more sweeping, executive order, a month ago.
The states of New York and Oregon said they would join the legal challenge.
Hawaii is already pursuing a separate case with a court hearing on March 15, the day before the revised ban comes into force.
White House spokesman Sean Spicer said he was "very confident" with how the revised executive order had been crafted.
Mr Ferguson said the state would ask judge Robart to rule that his temporary restraining order against the first ban applies to Trump's revised action.
Mr Trump's revised ban bars new visas for people from Somalia, Iran, Syria, Sudan, Libya and Yemen. It also temporarily shuts down the US refugee programme.
Unlike the initial order the new one says current visa holders will not be affected, and removes language that would give priority to religious minorities.
Mr Ferguson argued the travel ban is unconstitutional. He said it should be the court, rather than the government, that should decide whether the revised order is different enough from the first that it would not be covered by the previous temporary restraining order.
He said: "It cannot be a game of whack-a-mole for the court. That restraining order we've already obtained remains in effect."
Hawaii has said the revised order would harm its Muslim population, tourism and foreign students