New York, Washington, Oregon and Massachusetts have each launched opposition to the revised executive order - which places a 90-day ban on people from six mainly Muslim countries.
The new travel ban will come into force on March 16, with White House officials "very confident" of beating the legal action in court, BBC News reports.
Trump’s original executive order sparked widespread protests across the globe when it was introduced in January and was later defeated after a legal challenge initially mounted by judges Washington and Minnesota.
The revised ban prohibits new visas for citizens from: Somalia, Iran, Syria, Sudan, Libya and Yemen and also temporarily blocks all refugees.
Green Card holders from the six named countries will not be affected.
Iraq has been removed from the ban list because its government has boosted visa screening and data sharing, White House officials said.
It also lifts an indefinite ban on all Syrian refugees.
Eric Schneiderman, New York attorney general said: "President Trump’s latest executive order is a Muslim ban by another name, imposing policies and protocols that once again violate the Equal Protection Clause and Establishment Clause of the United State Constitution."
Washington state attorney general Bob Ferguson, who was the first to sue over the original travel ban, said he would urge federal judges to make sure the restrictions on the first immigration order "remains in effect" for the new version.
"We’re asserting that the president cannot unilaterally declare himself free of the court’s restraining order and injunction," he said.