The announcement comes on the last day of the court's term before summer recess.
In allowing parts of Trump's executive order to take effect, the court narrowed the scope of injunctions that lower courts put on the temporary travel ban.
The Supreme Court is allowing implementation of the temporary ban on entry into the U.S. of citizens of six Muslim-majority nations, with an exception for people who have what the court called "any bona fide relationship with a person or entity in the United States."
That includes foreign nationals with familial connections in the U.S., students who have already been admitted into an American university and workers with existing job offers in the U.S.
For people from the six countries who have such connections, the injunctions put in place by the lower courts are upheld. These individuals will not be barred under the executive order from coming into the U.S.
"What the Supreme Court did today was to significantly narrow the scope of the injunctions, limiting them to people with a bona fide connection to the U.S. This is an many ways a clever compromise," said Kate Shaw, ABC's Supreme Court contributor. "But it leaves open a number of questions of interpretation and implementation. I think it might lead to a lot of litigation over the summer about who exactly has enough of a connection to the U.S. to satisfy the Supreme Court's standard."
With today's court order, the travel ban is expected to go into effect in 72 hours, in accordance with an earlier White House memo saying that such a delay would "ensure an orderly and proper implementation."
After 72 hours, the 90-day ban for foreign nationals from the six countries who lack bona fide connections to the U.S. and the 120-day ban for refugees without such ties will start.
Understanding the court's action
The high court's action today was a per curium order, meaning that no author was identified, although three of the more conservative justices — Clarence Thomas, Samuel Alito and Neil Gorsuch — wrote separately that they supported going further by reversing the lower courts' injunctions in full and letting the ban go completely into effect.
Unlike the lower circuit courts that imposed stays and temporary restraining orders on the executive order, the Supreme Court didn't look at Trump's comments and tweets about Muslims. Today's order appeared focused on balancing the parties' interests, with its argument that Americans aren't sufficiently burdened if they have no connection to a foreign national seeking entry and that foreign nationals don't have a right to come in.
"Denying entry to such a foreign national does not burden any American party by reason of that party's relationship with the foreign national," the court order reads. It also says the travel ban would not "impose any legally relevant hardship on the foreign national himself."
The Supreme Court justices agreed with the 9th Circuit Court's ruling that the government may begin conducting a worldwide review of its procedures for vetting people seeking to come to the U.S. The court said the administration should have enough time to "conclude its internal work and provide adequate notice to foreign governments within the 90-day life" of the ban.
Trump and the ACLU react
Trump appeared to see the court order as a big victory.
"Today's unanimous Supreme Court decision is a clear victory for our national security," he stated.
"It allows the travel suspension for the six terror-prone countries and the refugee suspension to become largely effective. As president, I cannot allow people into our country who want to do us harm. I want people who can love the United States and all of its citizens and who will be hardworking and productive. My No. 1 responsibility as commander in chief is to keep the American people safe. Today's ruling allows me to use an important tool for protecting our nation's homeland. I am also particularly gratified that the Supreme Court's decision was 9-0," he said in the statement, again saying that there was a voted decision although there was not.
The American Civil Liberties Union, a party in the suit against what it calls a "Muslim ban," viewed the court order differently.
"President Trump's Muslim ban violates the fundamental constitutional principle that government cannot favor or disfavor any one religion. Courts have repeatedly blocked this indefensible and discriminatory ban. The Supreme Court now has a chance to permanently strike it down," said Omar Jadwat, the director of the ACLU's Immigrants' Rights Project.