The Justice Department is appealing a federal court's ruling against the Trump administration's temporary travel ban of refugees and residents of six majority-Muslim countries.
If the top court did not act, the ruling could have gone into effect as early as Tuesday.
A ruling of the 9th Circuit Court of Appeals pushed Trump on the back foot of travel ban on those refugees that have formal assurances from settlement agencies from entering the US.
In a one-page ruling, signed by Justice Anthony Kennedy, the Supreme Court announced that the exemption would be stayed pending a response from the state of Hawaii.
Since then, lawyers for Hawaii, which sued to block the ban, and the Trump administration have continued to fight over who is covered by those standards.
"This Court's ruling can not plausibly bear that construction, which would as a practical matter render the partial stay this Court granted as to the refugee provisions a dead letter", the administration said.
The Justice Department asked the Supreme Court to step in again - though only to block refugees, not grandparents and other extended family members.
The Justice Department wants to stay part of the appellate decision that said refugees should be allowed to enter if they have formal assurances from resettlement agencies that they will provide services when the refugees arrive.
The issue of the scope of the ban has been playing out in the lower courts, but the Supreme Court is set to hear the larger issues concerning the merits of the case on October 11. The district court also found that "grandparents, grandchildren, brothers-in-law, sisters-in- law, aunts, uncles, nieces, nephews, and cousins of persons in the United States" count as "close familial relationships" exempted from the travel ban.
Kennedy ordered challengers to the administration's refugee ban to submit written arguments in support of the lower court ruling by midday Tuesday. By that point, the original 90-day travel ban will have lapsed and the 120-day refugee ban will have just a few weeks to run.
The arguments hinged on a stipulation in the travel ban that refugees in the pipeline can only be accepted if they have a "bona fide relationship" with a United States individual or entity.