The ruling was one of a string of 5-4 decisions this term in which the justices on the right reasserted themselves, after the addition of Trump-nominated Justice Neil Gorsuch previous year restored a conservative majority.
The travel ban has been fully in place since December, when the justices stopped lower court decisions that had blocked part of it from being enforced.
The Supreme Court held that the challengers had failed to show that the travel ban violated either U.S. immigration law or the U.S. Constitution's First Amendment prohibition on the government favouring one religion over another. 'Public universities remain deeply concerned about this misguided travel ban and the message it sends to all worldwide students and scholars who have always been drawn to USA universities to undertake studies, conduct research and teach students at our world-leading institutions'. In an earlier paper statement, the president described the ruling as "a tremendous victory for the American People and the Constitution" as well as "a moment of profound vindication", taking aim at Democrats and the mainstream media who he said "refuse to do what it takes to secure our border and our country". Trump said in a White House statement. Writing for the majority, Chief Justice John Roberts said that the U.S. President has the Constitutional authority to block "entry of nationals who can not be adequately vetted". "We express no view on the soundness of the policy". In its latest version, which was issued in September 2017, the ban applied to those travelling from Syria, Libya, Iran, Yemen, Chad, Somalia, North Korea and Venezuela. "The victory of the Administration's policy to keep out legal immigrants is further proof that elections have consequences and that the Senate Republican strategy of denying a Democratic President appointments to the Supreme Court in order to allow court vacancies to be filled by a Republican President has worked".
The Supreme Court rejected a challenge that the policy discriminated against Muslims or exceeded Trump's authority.
During the presidential campaign, Trump called for a "total and complete shutdown of Muslims entering the United States until our country's representatives can figure out what is going on".
"We just have to know who's coming here", he said.
Ellison likened the 5-4 ruling in favor of the travel ban ruling to infamous decisions in the court's history, including one that allowed Japanese internment camps during World War II and another codifying the "separate but equal" doctrine of racial segregation.
But rights groups have denounced the decision.
The American Civil Liberties Union compared Tuesday's ruling to the 1944 Supreme Court decision that allowed the federal government to imprison Japanese Americans, calling both moves "shameful chapters of USA history". The ride-sharing company won a court case to continue operating after London's transport authority said it was not "fit and proper". During the April 25 arguments before the justices, Solicitor General Noel Francisco said it was "crystal clear" that the travel restrictions were not a manifestation of Trump's call for a Muslim ban.
In his remarks at the White House, Mr Trump reinforced his reasoning for the ban.
His lawyers said that only Trump's actions since he became president in January 2017 should be relevant to the case. It also halted refugee admissions for 120 days and indefinitely banned Syrian refugees.
The current travel ban dates from last September and it followed what the administration has called a thorough review by several federal agencies, although no such review has been shared with courts or the public. (The central African nation of Chad was initially included in the list but was later dropped).