The appeals court ruled that Trump had exceeded the authority Congress had given him over immigration and had violated a part of the immigration laws barring discrimination in the issuance of visas.
A case concerning the legality of a previous version of the ban was on the Court's calendar for earlier in the term but the justices removed it after the President issued this version of the travel ban in September.
The travel ban targets people from Chad, Iran, Libya, Somalia, Syria and Yemen who want to enter the U.S. It also places limits on travelers from Venezuela and North Korea.
The challenge accepted for oral argument is from Hawaii, where state officials have argued that the ban threatens their economy by blocking students, workers and others. The 4th Circuit appeals court, based in Virginia, is due to rule soon on the administration's appeal of that decision.
They prevailed before a US District Court in Hawaii and before a three-judge panel of the 9th US Circuit Court of Appeals in San Francisco. Judges have cited his derogatory tweets about Muslims as evidence that the ban was based on religious hostility. At the end of his first week in the White House, Trump signed a hastily crafted order that disrupted travel plans across the globe, triggered protests at airports across the nation and spurred a series of lawsuits.
A Justice Department spokesman declined to comment. Instead, they have argued that the administration's worldwide review of nations' immigration procedures established a legal basis for banning travelers from those considered to be threats to national security.More news: Myanmar police open fire and kill at least seven Buddhist protesters
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The law does not "surrender to the president a boundless authority to set the rules of entry and override the immigration laws at will", Katyal said in court papers.
The president had used the same argument to freeze all refugee admissions for 120 days, specifically focusing on Syrian refugees as having a heightened possibility of terrorist ties.
The Republican president has said the policy is needed to protect the United States from terrorism by Islamic militants.
A three-judge panel of judges on the 9th US Circuit Court of Appeals ruled past year that travel ban 3.0 exceeds the President's authority, calling it "an executive override of broad swaths of immigration laws that Congress has used its considered judgment to enact".
For people from the eight Muslim-majority countries named in any of Trump's three bans, there was a 41 percent drop in visas granted to enter the United States a year ago compared to before the bans were announced, government data showed.
The case represents a high-profile test of presidential powers.