In Maryland, a US judge will hear arguments from the American Civil Liberties Union (ACLU) and others who want to stop the new directive and more than a half-dozen states are trying to derail the executive order affecting travellers from six Muslim-majority nations.
Hawaii's lawsuit is heading to federal court in Honolulu, while Washington state, which successfully sued to block the original ban, wants its own hearing before a federal judge in Seattle. Five other states have joined Washington's challenge.
Here's a look at what's going on and the hurdles the new ban faces:
Hawaii will argue that the new order will harm its Muslim population, tourism and foreign students. Ismail Elshikh, a plaintiff in the lawsuit, said the ban will prevent his Syrian mother-in-law from visiting.
The federal government will argue that the allegations are pure speculation. Justice Department lawyers also say the president is authorised to restrict or suspend entry into the United States.
In Washington state, Attorney General Bob Ferguson is pushing for a hearing before Judge James Robart, who halted the original ban last month. Ferguson wants Robart to apply the ruling to the new ban.
Ferguson says the new order is unconstitutional and harms residents, universities and businesses, especially tech companies such as Washington state-based Microsoft and Amazon who rely on foreign workers. California, Maryland, Massachusetts, New York and Oregon have joined the claim. Federal lawyers say the revised travel ban is “substantially different” from the original directive.
Immigrant advocacy groups and the ACLU are also suing in Maryland. They will ask a judge there early Wednesday to issue an injunction, saying it's illegal to reduce the number of refugees in the middle of a fiscal year. The lawsuit is broader, but the ACLU expects a ruling on that part of the case even if other aspects of the ban are blocked elsewhere.
Washington and Hawaii say the order is an effort to carry out the Muslim ban he promised during his campaign and is a violation of the First Amendment, which bars the government from favouring or disfavouring any religion. On that point, they say, the new ban is no different than the old.
They point to statements by Trump's advisers, including former New York Mayor Rudy Giuliani, who said Trump asked him how to implement a Muslim ban legally, and Stephen Miller, who said the revised order was designed to have “the same basic policy outcome” as the first.
The new version tries to erase the notion that it was designed to target Muslims by detailing more of a national security rationale. It is narrower and eases some concerns about violating the due process rights of travellers.
It applies only to new visas from Somalia, Iran, Syria, Sudan, Libya and Yemen and temporarily shuts down the US refugee programme. It does not apply to travellers who already have visas.
The states' First Amendment claim has not been resolved. The 9th US Circuit Court of Appeals refused to reinstate the original ban but didn't rule on the discrimination claim.
Some legal scholars have said the order does not apply to all Muslims or even all predominantly Muslim nations - a point 9th Circuit Judge Richard Clifton made during arguments in Washington's case.
The administration says the travel ban is about national security. The revised order specifies that people from the listed countries “warrant additional scrutiny in connection with our immigration policies because the conditions in these countries present heightened threats.”
But intelligence analysts at the Department of Homeland Security have questioned that rationale, concluding that citizenship is an “unlikely indicator” of terrorist ties.
In addition, the states and civil liberties groups say US immigration law generally prohibits the government from discriminating based on nationality when issuing immigrant visas. The president cannot rewrite that law by executive order, the states say.
Some legal scholars have questioned whether states have standing to bring their cases, citing limits the Supreme Court has placed on when states can sue the federal government.
Michael McConnell, a constitutional law professor at Stanford Law School, has said he is “highly sceptical” that states can sue over this issue.
The 9th Circuit panel found that Washington and Minnesota, which is part of the original lawsuit, did have standing, at least at that early stage. The judges noted that some people would not enroll in universities or join the faculty, causing real harm for the states.
Hawaii focuses on an additional aspect: the loss of tourism, and thus tax dollars, in the heavily travel-dependent state.
“I don't think standing's a serious problem,” said Rory Little, a former Supreme Court clerk who teaches at the University of California Hastings College of the Law. “There's clearly harm to state budgets, harm to state universities.”
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