President Trump's decision to tap Matthew Whitaker as acting attorney general has "no effect" on an ongoing legal challenge to Robert Mueller's authority, prosecutors working for the special counsel said in a court filing on Monday.

Mueller's team addressed Whitaker's appointment in a supplemental brief filed in the case involving Andrew Miller, an associate of longtime Trump ally Roger Stone. Miller is currently fighting a subpoena to testify before the grand jury in the special counsel's Russia investigation.

Trump announced in early November that Whitaker would replace Jeff Sessions in an acting capacity after Sessions resigned as attorney general at the president's request. Some of Trump's critics have warned that Trump could be laying the groundwork to interfere in the Mueller investigation. Whitaker, who worked as Sessions's chief of staff, has in the past been critical of the probe.

A federal appeals court in D.C. had asked Mueller's team and Miller to each file briefs addressing what impact, if any, Whitaker's appointment would have on the ongoing legal battle. Both argued in separate filings that the appointment has no impact on the legal arguments in the case.

"Acting Attorney General Whitaker's designation neither alters the Special Counsel's authority to represent the United States nor raises any jurisdictional issue," Mueller's team wrote in the filing on Monday. "The Special Counsel continues to exercise the same authority, and the jurisdiction of the district court and this Court is intact."

Miller is challenging the constitutionality of Mueller's appointment, arguing that he should have been appointed by the president and confirmed by the Senate as a "principal officer," or otherwise should have been appointed as an "inferior officer" by Sessions - not by Deputy Attorney General Rod Rosenstein, who had been overseeing the probe up until Whitaker took the helm of the department earlier this month.

Lawyers representing Concord Management and Consulting, an organization accused of funding a Russian troll farm, unsuccessfully made a similar argument earlier this year in an attempt to dismiss an indictment filed by Mueller's team.

Mueller has an interest in Miller ostensibly for his connection to Stone, who has drawn scrutiny as a result of his public statements about WikiLeaks before the 2016 election. The special counsel has questioned a slew of Stone associates in an effort to determine what, if any, advanced knowledge anyone in Trump's orbit had of hacked Democratic emails leaked by WikiLeaks before Election Day.