Several US states have said they will move forward with legal challenges to President Donald Trump's revised executive order which targets citizens of six Muslim-majority countries and refugees.

Washington state, the first to sue over Trump's initial travel ban which created chaos worldwide and was eventually blocked, argued that the revised order violates the constitution "by disfavouring Islam".

Bob Ferguson, the state's attorney general, said a motion by his office calls on an existing injunction against the travel ban issued in January to be applied to the new directive.

"My message to President Trump is - not so fast," Ferguson said. "After spending more than a month to fix a broken order that he rushed out the door, the president's new order reinstates several of the same provisions and has the same illegal motivations as the original."

Attorney generals in the states of New York, Massachusetts and Oregon said they had taken steps to join the lawsuit that Washington had filed along with Minnesota.

The opposition comes on top of a separate legal challenge to the new ban brought by Hawaii.

READ MORE: What makes Trump's revised travel ban different?

The revised executive order issued on Monday bars new visas for people from Syria, Iran, Somalia, Libya, Sudan and Yemen, and temporarily shuts down the US refugee programme for 120 days.

It is supposed to go into effect on March 16, and does not apply to travellers who already have visas.

Oregon Attorney General Ellen Rosenblum said the executive order has hurt Oregon, its residents, employers, agencies, educational institutions, healthcare system and economy.

New York Attorney General Eric Schneiderman called the executive order "a Muslim ban by another name".

The attorney general in Hawaii argued that while the new order features changes to address complaints raised by courts that blocked the first travel ban, the new order is pretty much the same as the first one.

"Nothing of substance has changed: There is the same blanket ban on entry from Muslim-majority countries (minus one)," state attorney general Doug Chin said in a statement.

Hawaii's lawsuit says the order will harm Hawaii's Muslim population, tourism and foreign students.

White House spokesman Sean Spicer said Thursday the administration believed the revised travel ban will stand up to legal scrutiny.

"We feel very confident with how that was crafted and the input that was given," Spicer said.

A federal judge in Seattle issued a temporary restraining order halting the initial ban after Washington state and Minnesota sued. The 9th US Circuit Court of Appeals refused to reinstate the order.

University of Richmond Law School professor Carl Tobias said Hawaii's complaint seemed in many ways similar to Washington's successful lawsuit, but whether it would prompt a similar result was hard to say.

Given that the new executive order spells out more of a national security rationale than the old one and allows for some travellers from the six nations to be admitted on a case-by-case basis, it will be harder to show that the new order is intended to discriminate against Muslims, Tobias said.

"The administration's cleaned it up, but whether they have cleaned it up enough I don't know," he said. "It may be harder to convince a judge there's religious animus here."

Tobias also said it is good that Hawaii's lawsuit includes an individual plaintiff, considering that some legal scholars have questioned whether the states themselves have standing to challenge the ban.

Imam Ismail Elshikh of the Muslim Association of Hawaii is a plaintiff in the state's challenge. He says the ban will prevent his Syrian mother-in-law from visiting him.