"We have always known this case would ultimately be decided by the United States Supreme Court", said Hawaii Attorney General Doug Chin.
The legal fight over Trump's travel ban has simmered through his first year in office.
The first executive order restricting travel was signed nearly a year ago, on January 27.
The latest of those rulings came last month when the federal appeals court in San Francisco ruled that the travel ban Trump announced in September violates federal immigration law. More recently, the legal battles have focused tightly on the provisions of US immigration law.
The Justice Department did not file an emergency application that, if successful, would result in the judge's ruling being put on hold within days.
The justices briefly grappled in June with the second version of the travel ban.
And on December 4, the justices took the unusual step of sweeping aside the injunctions handed down by several judges and allowing Trump's full travel ban to take effect, even though the cases were about to be heard by two appeals courts.
That move suggested the court's conservatives were exasperated by liberal trial judges issuing sweeping nationwide orders that rejected the president's plan.
Even Eyelashes Freeze as Russia Sees Temperatures Hit Minus 67 C
According to NASA , the lowest temperature ever recorded was -133.6 Fahrenheit, in a hollow in Antarctica in August 2010. And although students routinely go to school when it's 40 below, school was canceled throughout the region this week.
The New York Times reported that in September a year ago a USA court ruled that the ban was tainted by "religious animus (hostility)" and was not adequately justified by national security concerns.
Their best hope may lie with a close reading of conflicting provisions in immigration laws.
"The immigration laws do not grant the President this power", Katyal said.
Solicitor General Noel Francisco said in court papers that the policy is well within the president's "broad authority to suspend or restrict the entry of aliens outside the United States when he deems it in the Nation's interest".
The administration is challenging a January 9 decision by San Francisco-based U.S. District Judge William Alsup, who ruled that DACA must remain in place while the litigation is resolved.
A couple weeks later, the U.S. Court of Appeals ruled - again - that the ban was illegal. The judges in a 3-0 decision noted Trump's order no longer was portrayed as an urgent, temporary measure that gave time for the new administration to revise the "vetting procedures" for foreign travelers.
Lower courts in California, Hawaii and other states have repeatedly ruled that Trump's order targets Muslims in violation of the US Constitution.
Opponents say it is unconstitutional and discriminatory and that in making it Mr Trump has exceeded his legal authority.