The latest iteration, the third ban that Trump has ordered, blocks various people from Syria, Libya, Iran, Yemen, Chad, Somalia, North Korea and Venezuela. Six of the countries have Muslim majorities.
But federal judges in Maryland and Hawaii have blocked its implementation for "foreign nationals who have a credible claim of a bona fide relationship with a person or entity in the United States". They said such people include grandparents, grandchildren, brothers-in-law, sisters-in-law, aunts, uncles, nieces, nephews and cousins of people in the United States.
The language is drawn from a Supreme Court decision last June that exempted such foreign nationals from Trump's second version of the executive order, which expired this autumn.
Lawyers for Hawaii, one of the challengers to the travel bans, said there was no reason for the Supreme Court to back away from the "equitable determination, dutifully adhered to by the court below," that it had already made.
If anything, it said, the government's case has weakened.
Instead of previous temporary travel bans, the president now "has imposed an indefinite one, deepening and prolonging the harms a stay would inflict," says the brief submitted on Hawaii's behalf by Washington lawyer Neal K. Katyal.
"The government's national security rationales have also grown more attenuated: The order itself acknowledges that the affected aliens can safely be vetted and granted entry, so long as they seek visas the government prefers, and the government's delay in requesting a stay makes plain that no exigency warrants this court's immediate intervention."
Solicitor General Noel J. Francisco, representing the Trump administration, argued just the opposite.
The new executive order, he wrote, followed a "comprehensive, worldwide review of the information shared by foreign governments that is used to screen aliens seeking entry to the United States.
"Based on that review, the proclamation adopts tailored entry restrictions to address extensive findings that a handful of particular foreign governments have deficient information-sharing and identity-management practices, or other risk factors."
The Supreme Court's actions do not affect lower courts' consideration of the merits of challenges to the travel ban.
In his brief, Francisco says the administration's thorough review "conclusively rebuts respondents' claims that the entry restrictions were motivated by animus rather than protecting national security."
But Francisco's arguments might be complicated by the president's recent actions, such as sharing on Twitter three inflammatory anti-Muslim videos posted by a far-right British activist.
Federal judges have frequently cited Trump's remarks as they have blocked various versions of the ban, and lawyers for those suing over the latest iteration of the directive seized immediately on the president's early morning online posts.
"Thanks! See you in court next week," wrote Katyal.
