In a court filing, the administration asked the justices to overturn Thursday's decision by a US district judge in Hawaii, which limited the scope of the administration's temporary ban on refugees and travelers from six Muslim-majority countries.
The latest round in the fight over Trump's March 6 executive order, which he says is needed for national security reasons, came after the Supreme Court intervened last month to partially revive the two bans, which were blocked by lower courts.
The Supreme Court said then that the ban could take effect, but that people with a "bona fide relationship" to a US person or entity could not be barred.
The administration had narrowly interpreted that language, saying the ban would apply to grandparents and other family members, prompting the state of Hawaii to ask Hawaii-based US District Judge Derrick Watson to expand the definition of who could be admitted. He ruled for the state late on Thursday.