A sharply divided Supreme Court on Tuesday upheld President Donald Trump's ban on travel from several mostly Muslim countries, rejecting a challenge that it discriminated against Muslims or exceeded his authority. However, a dissenting justice said the outcome was a historic mistake.

The 5-4 decision on Tuesday is a big victory for Trump on an issue that is central to his presidency, and the court's first substantive ruling on a Trump administration policy. The president quickly tweeted his reaction: “Wow!” Chief Justice John Roberts wrote the majority opinion for the five conservative justices, including Trump nominee Neil Gorsuch.

Roberts wrote that presidents have substantial power to regulate immigration. He also rejected the challengers' claim of anti-Muslim bias.

But he was careful not to endorse either Trump's provocative statements about immigration in general or Muslims in particular, including Trump's campaign pledge to keep Muslims from entering the country. “We express no view on the soundness of the policy,” Roberts wrote.

The travel ban has been fully in place since December when the justices put the brakes on lower court rulings that had ruled the policy out of bounds and blocked part of it from being enforced.

In a dissent she summarised in court, Justice Sonia Sotomayor said, “History will not look kindly on the court's misguided decision today, nor should it.” Justices Stephen Breyer, Ruth Bader Ginsburg and Elena Kagan also dissented.

Sotomayor wrote that based on the evidence in the case “a reasonable observer would conclude that the Proclamation was motivated by anti-Muslim animus.”

She said her colleagues in the majority arrived at the opposite result by “ignoring the facts, misconstruing our legal precedent and turning a blind eye to the pain and suffering the Proclamation inflicts upon countless families and individuals, many of whom are United States citizens.”

She likened the case to the discredited Korematsu V. US decision that upheld the detention of Japanese-Americans during World War II. Roberts responded in his opinion that “Korematsu has nothing to do with this case” and “was gravely wrong the day it was decided.”

The travel ban was among the court's biggest cases this term and the latest in a string of 5-4 decisions in which the conservative side of the court, bolstered by the addition of Gorsuch last year, prevailed. Gorsuch was nominated by Trump after Republicans in the Senate refused to grant a hearing to federal appeals Judge Merrick Garland, who was appointed by Barack Obama with more than 10 months remaining in Obama's term.