The US government on Monday defended President Donald Trump's travel ban as a "lawful exercise" of his authority, and claimed that a federal court made a mistake in barring enforcement of the measure.

"The executive order is a lawful exercise of the president's authority over the entry of aliens into the United States and the admission of refugees," read a brief filed by Justice Department lawyers to the Ninth Circuit Court of Appeals.

"The district court therefore erred in entering an injunction barring enforcement of the order. But even if some relief were appropriate, the court's sweeping nationwide injunction is vastly overbroad," it said.

The government again asked that the ban be reinstated. A hearing has been set in the case for Tuesday at 3:00 pm Pacific time (2300 GMT).