Trump wants to ban citizens from six mostly Muslim countries from travelling to the US.
Justice Department lawyers have asked the Supreme Court to overturn a decision of the full US Court of Appeals for the 4th Circuit that kept in place a freeze on Trump’s revised ban, the Independent reports.
The ruling last week was one in a series of legal defeats for the administration.
The government’s filing this week asks the justices to set aside the 4th Circuit ruling and accept the case for oral arguments.
It also asks the high court to lift a nationwide injunction issued by a federal judge in a separate Hawaii case.
The president’s travel order has been one of the most controversial of the Trump administration, as the first entry ban created chaos at airports around the world and prompted major protests.