In a one-paragraph order, the three-judge panel of the U.S. Court of Appeals for the District of Columbia Circuit told Mueller's team it has until Nov. 19 to turn in supplemental briefs explaining "what, if any, effect" Sessions' exit Wednesday has on the Justice Department's Russia investigation.
Mueller has been investigating potential Russian involvement and collusion by the Trump campaign in the 2016 U.S. presidential election. He has been conducting the inquiry without Sessions, who recused himself from the case over possible conflicts of interest.
Deputy Attorney General Rod Rosenstein has acted as Mueller's supervisor since March 2017. After Sessions' firing, Trump quickly appointed Matt Whitaker as acting attorney general.
The shakeup at the Department of Justice led to calls for Whitaker's recusal of the Mueller investigation, due to past statements from Whiteaker about the validity of the investigation. Whitaker also has ties to Andrew Miller, who's been called as a witness before a grand jury.
Miller was an aide to former Trump adviser Roger Stone, who is challenging Mueller's appointment to the case on constitutional grounds. Miller's legal team was given a similar order by the court for a legal brief regarding the impact of Sessions' firing and Whitaker's appointment.
Whitaker has offered no indication that he will recuse himself.
"We don't discuss recusals but there is no reason to think that is the case," a Justice Department spokeswoman said after Sessions left Wednesday.
Friday, Judge Karen LeCraft Henderson instructed attorneys to disregard Sessions' removal and treat the hearing "as if it were argued yesterday morning." The hearing largely involved whether Mueller's appointment as special counsel was constitutionally lawful, but also included a demand by the court for comments about the change in leadership.
Trump's appointing Whitaker as acting attorney general is counter to the usual line of succession in the Justice Department. Senate Minority Leader Charles Schumer, D-N.Y., warned in a letter to Trump Friday that it potentially violated the Appointments Clause of the U.S. Constitution.
"Whitaker is a political appointee who is not serving in a Senate confirmed position in the Justice Department," Schumer wrote. "I am not aware of any precedent for appointment of an official who has not been confirmed by the Senate to serve as acting Attorney General."
Schumer added that Whitaker's rise to the temporary post "raises a number of questions regarding the propriety and even the constitutionality of that action."