Family members who have just arrived Monday from Syria are greeted by family who live in the United States upon their arrival at JFK International Airport in New York.

WASHINGTON — The fierce battle over President Donald Trump's travel and refugee ban edged up the judicial escalator Monday, headed for a possible final face-off at the Supreme Court. Travelers, temporarily unbound, tearfully reunited with loved ones at U.S. airports.

The Justice Department prepared to ask a San Francisco-based federal appeals court to restore Trump's ban on travelers from seven predominantly Muslim nations. The lawyers were expected to argue in a brief that the president, not the courts, has the authority to set national security policy and that an executive order to control access at the country's borders is lawful.

The filing with the 9th U.S. Circuit Court of Appeals was to be the latest salvo in a high-stakes legal fight surrounding Trump's order, which was halted Friday by a federal judge in Washington state.

The appeals court refused to immediately reinstate the ban, and lawyers for Washington and Minnesota — two states challenging it — argued anew on Monday that any resumption would “unleash chaos again,” separating families and stranding university students.

It's not clear how quickly the appeals court might rule. Whatever the outcome, either side could ask the Supreme Court to intervene.

It could prove difficult, though, to find the necessary five votes at the high court to undo a lower court order; the Supreme Court has been at less than full strength since Justice Antonin Scalia's death a year ago. The last immigration case that reached the justices ended in a 4-4 tie.

The president's executive order has faced legal uncertainty ever since Friday's ruling by U.S. District Judge James Robart, which challenged both Trump's authority and his ability to fulfill a campaign promise.

The State Department quickly said people from the seven countries — Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen — could travel to the U.S. if they had valid visas. The Homeland Security Department said it was no longer directing airlines to prevent affected visa holders from boarding U.S.-bound planes.

The legal fight involves two divergent views of the role of the executive branch and the court system. The government says the president alone has the power to decide who can enter or stay in the United States, while Robart said a judge's job is to ensure that an action taken by the government “comports with our country's laws.”

His Friday ruling triggered a Twitter rant by Trump, who dismissed Robart as a “so-called judge.”