BBC, March 10, 2017
Mr Trump signed an executive order placing a 90-day ban on people from six mainly Muslim countries on Monday.
New York maintains the new directive is a ban on Muslims while Washington says it is harmful to the state. Oregon and Massachusetts later also joined.
The ban begins on 16 March, with the White House saying it is “very confident” of winning in court.
Mr Trump’s original order was more expansive but it was defeated after a legal challenge initially mounted by Washington and Minnesota.
Lawyers for those states say their original complaint applies to the revised order and are pursuing their cases.
Other states have joined the bid too, while Hawaii has launched a separate action.
Which states have launched challenges and why?
Oregon – said the order hurts residents, employers, universities health care system and economy
Washington – it has “same illegal motivations as the original” and harms residents, although fewer than the first ban
Minnesota – questioned the legality of the move, suggesting the Trump administration can’t override the initial ban with a fresh executive order
New York – “a Muslim ban by another name”, said the attorney general
Massachusetts – new ban “remains a discriminatory and unconstitutional attempt to make good on his campaign promise to implement a Muslim ban”
Hawaii – argued it would harm its Muslim population, tourism and foreign students
The revised ban bars new visas for people from: Somalia, Iran, Syria, Sudan, Libya and Yemen. It also temporarily blocks all refugees.
The previous order, which Mr Trump signed in January, was blocked in federal courts and sparked mass protests as well as confusion at airports.
But critics maintain the revised travel ban discriminates against Muslims.
“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,” said New York Attorney General Eric T Schneiderman after announcing his legal challenge.
Washington state Attorney General Bob Ferguson, who was the first to sue over the original ban, said he would ask a federal judge to rule that the temporary restraining order halting the first travel ban “remains in effect”.
“We’re asserting that the president cannot unilaterally declare himself free of the court’s restraining order and injunction,” he said.
Though the White House has faced mounting criticism over its immigration orders, Trump supporters say the president is fulfilling his campaign promises to protect Americans.
Citizens of Iran, Libya, Syria, Somalia, Sudan and Yemen, the other six countries on the original 27 January order, will once more be subject to a 90-day travel ban.
Iraq has been taken off the banned list because its government has boosted visa screening and data sharing, White House officials said.
The new directive says refugees already approved by the State Department can enter the US. It also lifts an indefinite ban on all Syrian refugees.
Green Card holders (legal permanent residents of the US) from the named countries will not be affected.
The new order does not give priority to religious minorities, unlike the previous directive.
Critics of the Trump administration had argued that this was an unlawful policy showing preference to Christian refugees.