In a court filing on Friday, 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 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.
"Common sense, for instance, dictates that close family members be defined to include grandparents," US District Judge Derrick Watson said in his ruling, Al Jazeera reported.
"Indeed grandparents are the epitome of close family members."
In the court filing, the Justice Department said Watson's ruling on refugees would make the Supreme Court's decision on that part of the executive order "effectively meaningless".
The ruling, if left in place, means refugees can continue to be resettled in the United States, beyond a cap of 50,000 set by the executive order.
That limit was reached this week.
The Supreme Court's decision last month revived parts of Trump's March 6 executive order banning travelers from Iran, Libya, Somalia, Sudan, Syria and Yemen for 90 days, as well as refugees for 120 days.
The Trump administration then decided that spouses, parents, children, fiances and siblings would be exempt from the ban, but not grandparents and other family members travelling from those countries.
The Trump administration also said that all refugees without a close family tie would be blocked from the country for four months.