WASHINGTON (Reuters) - A federal appeals court that is weighing a legal challenge to Special Counsel Robert Mueller’s authority said Friday it wanted to know whether the sudden ouster of Attorney General Jeff Sessions could impact or change the outcome of how it should rule.

The court’s order directed each party in the case to file briefs by Nov. 19 outlining, “what, if any effect, the November 7, 2018 designation of an Acting Attorney General different from the official who appointed Special Counsel Mueller has on this case.”

The order came one day after a three-judge panel for the U.S. Court of Appeals for the District of Columbia Circuit heard oral arguments on whether Mueller was unlawfully appointed by Deputy Attorney General Rod Rosenstein in May 2017 and wielded too much power.

The challenge to Mueller’s authority was being brought by Andrew Miller, an associate of President Donald Trump’s long-time political adviser, Roger Stone.

Several of Stone’s associates have been subpoenaed by a grand jury in recent months, as part of Mueller’s probe into whether Trump’s campaign colluded with Russia.

Trump has called the investigation a witch hunt, and both he and Russia deny colluding.

Miller defied the subpoena in May, was later held in civil contempt, and filed a lawsuit alleging that Mueller’s appointment violated the U.S. Constitution and also that Rosenstein had no authority to hire him.

Mueller was named special counsel by Rosenstein after Sessions recused himself from the probe. However, Rosenstein lost his role as Mueller’s supervisor on Wednesday after Trump forced Sessions to resign and replaced him with Matt Whitaker.

As acting attorney general, Whitaker has assumed oversight of the Mueller investigation.

Democrats have called on Whitaker to recuse himself as he has previously made negative comments about the probe.