Justices Samuel A. Alito Jr. and Clarence Thomas, as they have in the past, said they did not believe the court had the authority to simply reject Texas’s request. I would therefore grant the motion to file the bill of complaint but would not grant other relief, and I express no view on any other issue.

Trump, who has appointed three of the court’s nine members, has long viewed the Supreme Court as something of an ace-in-the-hole, and called for the justices to display courage and rescue him in post-election litigation.

After Justice Ruth Bader Ginsburg died in September, he said filling the seat was essential because of the possibility of litigation that might otherwise end in a tie. Justice Amy Coney Barrett was confirmed in a party-line vote by the Republican-controlled Senate to replace Ginsburg.

In a case earlier this week, the court turned down a request from Republican congressional candidates to overturn the the results in Pennsylvania in a one-sentence order. Barrett took part in the case, but neither she nor fellow Trump appointees Neil M. Gorsuch or Brett M. Kavanaugh noted their objection.”