In its filing, the government asked the top US court to rule on the legal standing of Trump's order, appealing a ruling by the federal Fourth Circuit Court of Appeals that upheld a nationwide block of the travel ban.
It also asked the Supreme Court to lift another US-wide injunction issued by a federal judge in a separate case based in Hawaii. That case is currently before the Ninth Circuit Court of Appeals, where a decision is pending.
The administration is "confident that President Trump's executive order is well within his lawful authority to keep the nation safe and protect our communities from terrorism," Justice Department spokeswoman Sarah Isgur Flores said.
"The president is not required to admit people from countries that sponsor or shelter terrorism, until he determines that they can be properly vetted and do not pose a security risk to the United States."
The filing came one week after the Fourth Circuit Court of Appeals ruling dealt a fresh blow to Trump's efforts to push the controversial travel ban that has triggered mass protests and confusion at airports.
The Fourth Circuit said it "remained unconvinced" that the part of the measure naming the specific countries -- Iran, Libya, Somalia, Sudan, Syria and Yemen -- had "more to do with national security than it does with effectuating the president's promised Muslim ban."
- "Indisputably high" stakes -
It said it was unclear whether the government's security concerns outweighed the plaintiffs' concerns about discrimination.
The government's filing acknowledged that stakes "are indisputably high."
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The Court of Appeals "concluded that the president acted in bad faith with religious animus when, after consulting with three members of his cabinet, he placed a brief pause on entry from six countries that present heightened risks of terrorism," the filing read.
That court's decision "creates uncertainty about the president's authority to meet those threats as the Constitution and acts of Congress empower and obligate him to do."
Even if the Supreme Court takes the case, it is unlikely to hear it this term, which is due to end this month.
Trump issued his initial travel ban by executive order in January, but that measure -- which banned entry to nationals from seven countries for 90 days and suspended the nation's refugee program for 120 days -- was quickly halted by the courts.
The administration said the travel ban was needed so it could evaluate existing screening methods protocols and set new ones.
A revised executive order in March meant to address concerns raised by the federal judges. It deleted Iraq from the list and removed an indefinite ban on Syrian refugees.
The order however was widely criticized, including by human rights activists and US states led by Democrats.
Federal judges in Maryland and Hawaii issued a nationwide block on the measure, sending the issue to the relevant appellate courts.
Given the case's high-profile nature, the full Fourth Circuit Court of Appeals in Virginia heard the arguments last week -- bypassing the usual initial three-judge panel -- for the first time in a quarter of a century.
Thirteen of the court's 15 active judges took part. Two recused themselves over potential conflicts of interest.