"We look forward to the Court's review of this important case," said lawyer Neal Katyal, who has represented the state of Hawaii in its efforts to block the travel order.
Like earlier versions of the travel order, this one has become hung up in legal fights in the courts, though the Supreme Court ruled in December that the Trump Administration could enforce the ban while appeals are underway.
A federal appeals court in San Francisco - the Ninth Circuit - struck down the travel ban last month.
There is also a separate challenge against the President's travel order going before the Fourth Circuit.
The plan limits travel from Yemen, Syria, Chad, Libya, Iran, and Somalia.
This is the third version of the President's travel order - the first one, almost a year ago in late January of 2017, caused an uproar at airports in the United States, and was put on hold by a series of federal judges, after protests at airports over people who were denied entry to the U.S., even though they had legal visas and paperwork to visit.
A second travel order was issued less than two months later. It ultimately went into effect partially, as administration attempts to limit family visits from certain countries was re-tooled in the courts.
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