– Special counsel Robert Mueller's team defended the validity of his appointment in court Thursday amid uncertainty about the future of his investigation into Russian interference in the 2016 presidential election.

Mueller's attorneys were responding to a challenge brought by an associate of Roger Stone, a longtime adviser to President Donald Trump, that questions the constitutionality of Mueller's role — and that could eventually reach the Supreme Court.

The hearing, coming a day after Trump ousted Attorney General Jeff Sessions, opened with a judge at the U.S. Court of Appeals for the District of Columbia Circuit telling lawyers to make their case as if it were being argued before the Justice Department shake-up.

Andrew Miller, a former assistant to Stone, appealed after losing his bid to block a grand-jury subpoena from Mueller. Miller was held in contempt, but that ruling is on hold pending his appeals case.

The special counsel's team has sought to interview Stone associates or have them appear before the grand jury as part of the 18-month-old probe.

Government attorney Michael Dreeben provided insight Thursday into how Mueller's team has been operating under the supervision of Deputy Attorney General Rod Rosenstein. There is day-to-day independence, but the team has to report major developments, he said. Rosenstein can ask for explanations of prosecutorial decisions, and the team needs approval to grant immunity to witnesses, for instance, or to subpoena a member of the media.

"He's aware of what we're doing," Dreeben said in court. "It is not the case that the special counsel's office is off wandering in a free-floating environment."

Miller's attorney disagreed. He said Mueller was named unlawfully, in violation of the appointments clause of the Constitution, arguing that he has broad prosecutorial powers and little oversight. Mueller "lacks significant direction and supervision" and is akin to a U.S. attorney-at-large, argued Miller attorney Paul Kamenar.

Miller's appeal is backed by the National Legal and Policy Center, a conservative nonprofit group, and was shaped in part by arguments advanced by law professor Steven Calabresi, co-founder of the Federalist Society.

Two district court judges — one nominated by a Democrat, the other by Trump — have upheld the constitutionality of Mueller's appointment in recent rulings. The hearing Thursday, however, was the first time an appeals court panel — made up of Judges Karen LeCraft Henderson, Judith Rogers and Sri Srinivasan — reviewed the special counsel's authority.