A panel of three judges on the D.C. Circuit Court of Appeals heard arguments on Thursday over the constitutionality of Robert Mueller's appointment as special counsel. The hearing regarded an appeal brought by lawyers for Andrew Miller, an aide to Roger Stone who challenged a subpoena from Mueller to testify before a federal grand jury and was held in contempt of court.

The question before the court was whether Mueller's appointment by Rod Rosenstein was lawful. Paul Kamenar, a lawyer for Miller, argued Mueller's appointment fell outside the scope of the deputy attorney general's authority and would only be valid if Mueller has been nominated by the president and confirmed by the Senate. Kamenar said Mueller was acting essentially as a "U.S. attorney-at-large" who "exercise[s] principal-officer powers."

Judge Karen LeCraft Henderson began the hearing by instructing the attorneys to disregard Sessions' ousting on Wednesday and treat the hearing "as if it were argued yesterday morning." The judges indicated they would request some sort of supplemental briefing on how Sessions' departure impacts the case. The special counsel's activities now fall under the purview of Acting Attorney General Matthew Whitaker, who has given no indication he intends to recuse himself from the case.

In a line of questioning by Judge Sri Srinivasan, Kamenar argued that Mueller's office has an "expanded" jurisdiction and lacks "meaningful supervision" by the Justice Department.

"That's what this whole case is about: political accountability," Kamenar said.

Michael Dreeben, arguing on behalf of the special counsel, defended the appointment and maintained that Mueller's office is part of "a much tighter regulatory nexus." Citing testimony by Rosenstein before Congress, Dreeben told the judges "the special counsel has a regular reporting obligation to the acting attorney general."

He also shed some light on the relationship between the DOJ and the special counsel's office.

"[Rosenstein] is aware of what we're doing," Dreeben said. He said Mueller's team is "independent on a day-to-day basis," and added that if Rosenstein found anything to be "inappropriate" or "unwarranted," he would intervene.

The argument put forth by Miller's legal team challenges Rosenstein's status as acting attorney general on matters related to the Russia investigation. The attorneys argued Sessions did not relinquish his constitutional duty to appoint "inferior" officers when he recused himself.

Rosenstein appointed Mueller in May 2017 as "Special Counsel to Investigate Russian Interference with the 2016 Presidential Election and Related Matters." The appointment order laid out the office's mandate and the scope of the investigation in accordance with DOJ regulations on special counsels.

Dreeben noted that it would be a "little odd" if statutes authorizing the DOJ to appoint special attorneys did not cover the naming of special counsels. One section of the relevant law reads, "Each Attorney specially retained under the authority of the Department of Justice shall be commissioned as special assistant to the Attorney General or special attorney, and shall take the oath required by law."

Some of the biggest scandals in American history were investigated by special counsels, Dreeben reminded the court. However, James Martin, an attorney for Concord Management and Consulting who appeared in court to support Miller's effort, argued no statute exists delegating the power Mueller has wielded in prosecutions across jurisdictions.

"The special counsel is a private lawyer," Martin said. "There is no grant of authority ... to appoint a person in Mueller's position."

Concord Management and Consulting is one of the three Russian companies indicted in connection to the Russia investigation. In June, the firm moved to dismiss the case, citing Mueller's "unlawful appointment and lack of authority."

In August, Judge Dabney Friedrich, a Trump appointee, denied Concord's request. "Even though no statute explicitly authorizes the Acting Attorney General to make the appointment, Supreme Court and D.C. Circuit precedent make clear that the Acting Attorney General has the necessary statutory authority," she wrote.

Friedrich is one of two district court judges who have already ruled that Mueller's appointment was constitutional. The other request to dismiss was brought by Paul Manafort, who pleaded guilty in September and is now cooperating with the special counsel.

Miller's attorney welcomed the opportunity to bring his case to the Supreme Court, should the current appeal fail. Kamenar was brought on by the National Legal Policy Center, which sought out Miller as a vehicle to challenge the special counsel's authority. Miller himself was not present in court Thursday.

In August, Chief Judge Beryl Howell held Miller in contempt for refusing to comply with subpoenas to appear before the Mueller grand jury in Washington, D.C. The contempt order has been put on hold during the appeals process.

Stone, a former adviser to President Trump, communicated with Russian hackers operating under the Guccifer 2.0 alias and allegedly communicated with WikiLeaks founder Julian Assange. He is also reported to have met with a Russian national who claimed to have dirt on Hillary Clinton, but insisted in testimony before the House Intelligence Committee in September 2017 that he did not collude with Russia.

Kamenar said the "constitutional doubt" surrounding Mueller may become irrelevant if Stone is indicted and Mueller withdraws his subpoena of Miller.

Brianna Borghi contributed to this report.