One of the main concerns is allegations by the states, civil rights groups, some lawmakers and citizens that the order discriminates in violation of the constitution's First Amendment, which prohibits favoring one religion over another.

The judges will have to decide whether to look exclusively at the actual text of the president's order, which does not mention any particular religion, or consider outside comments by Trump and his team to discern their intent.

Washington state's attorney Noah Purcell told the hearing that even though the lawsuit is at an early stage, the amount of evidence that Trump intended to discriminate against Muslims is "remarkable." It cited Trump's campaign promises of a "total and complete shutdown of Muslims entering the United States."