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 controversial orders Donald Trump has already issued
The controversial orders Donald Trump has already issued
1/9 Trump and the media
White House Press Secretary Sean Spicer takes questions during the daily press briefing
2/9 Trump and the Trans-Pacific Partnership
Union leaders applaud US President Donald Trump for signing an executive order withdrawing the US from the Trans-Pacific Partnership negotiations during a meeting in the Roosevelt Room of the White House in Washington DC. Mr Trump issued a presidential memorandum in January announcing that the US would withdraw from the trade deal
3/9 Trump and the Mexico wall
A US Border Patrol vehicle sits waiting for illegal immigrants at a fence opening near the US-Mexico border near McAllen, Texas. The number of incoming immigrants has surged ahead of the upcoming Presidential inauguration of Donald Trump, who has pledged to build a wall along the US-Mexico border. A signature campaign promise, Mr Trump outlined his intention to build a border wall on the US-Mexico border days after taking office
4/9 Trump and abortion
US President Donald Trump signs an executive order as Chief of Staff Reince Priebus looks on in the Oval Office of the White House. Mr Trump reinstated a ban on American financial aide being granted to non-governmental organizations that provide abortion counseling, provide abortion referrals, or advocate for abortion access outside of the United States
5/9 Trump and the Dakota Access pipeline
Opponents of the Keystone XL and Dakota Access pipelines hold a rally as they protest US President Donald Trump's executive orders advancing their construction, at Columbus Circle in New York. US President Donald Trump signed executive orders reviving the construction of two controversial oil pipelines, but said the projects would be subject to renegotiation
6/9 Trump and 'Obamacare'
Nancy Pelosi who is the minority leader of the House of Representatives speaks beside House Democrats at an event to protect the Affordable Care Act in Los Angeles, California. US President Donald Trump's effort to make good on his campaign promise to repeal and replace the healthcare law failed when Republicans failed to get enough votes. Mr Trump has promised to revisit the matter
7/9 Donald Trump and 'sanctuary cities'
US President Donald Trump signed an executive order in January threatening to pull funding for so-called "sanctuary cities" if they do not comply with federal immigration law
8/9 Trump and the travel ban
US President Donald Trump has attempted twice to restrict travel into the United States from several predominantly Muslim countries. The first attempt, in February, was met with swift opposition from protesters who flocked to airports around the country. That travel ban was later blocked by the Ninth Circuit Court of Appeals. The second ban was blocked by a federal judge a day before it was scheduled to be implemented in mid-March
SANDY HUFFAKER/AFP/Getty Images
9/9 Trump and climate change
US President Donald Trump sought to dismantle several of his predecessor's actions on climate change in March. His order instructed the Environmental Protection Agency to reevaluate the Clean Power Plan, which would cap power plant emissions
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.”