BOSTON — Lawyers for former Maine House Speaker Mark Eves and for Gov. Paul LePage squared off Tuesday before a panel of federal judges who will decide whether Eves’ lawsuit against the governor should go forward.

Eves was fired in 2016 as president of the Good Will-Hinckley School after LePage threatened to withhold funding for the Maine Academy of Natural Sciences, a public charter school for at-risk students run by Good Will-Hinckley. Eves said the governor’s actions violated his constitutional rights and he sued.

But the suit was dismissed last year by a federal judge in Maine, who ruled that the governor had immunity from lawsuits over funding decisions.

A three-judge panel of the 1st U.S. Circuit Court of Appeals in Boston then backed the Maine judge’s ruling. But this year, a majority of the full appeals court took the unusual step of setting aside the panel’s ruling and holding a hearing before the entire appeals court.

The court rarely hears such appeals “en banc,” or before the full court. The 1st Circuit Court had done so four times over the last five years, according to a recent study.

David Webbert, Eves’ lawyer, was closely questioned over the relationship between Good Will-Hinckley, which hired Eves as president in 2016, and the Maine Academy of Natural Sciences, which is overseen by Good Will-Hinckley but has a separate board. The academy is a charter school that is technically a private school, but receives a mix of public and private funds.

LePage had threatened to withdraw funding for the academy after Eves was hired, saying Eves’ previous opposition to charter schools made him unfit for the position.

LePage, a Republican, was usually at odds with Eves, a Democrat, in Augusta. Eves is running for governor this year, a position LePage can no longer seek because of term limits.

Webbert sought to let the judges know about Maine’s rancorous political atmosphere, saying he wasn’t aware of any other Maine governor who “threatened to veto every bill from a Democrat,” as LePage has done. That played into the dispute over funding, he said, because LePage didn’t want to send money to a school linked with a political enemy. But if Eves were president of Good Will-Hinckley, a private school, Webbert said LePage had no expectation that Eves “would owe a pledge of loyalty” to the governor.

But Patrick Strawbridge, LePage’s lawyer, said the issue is the governor’s immunity from lawsuits over funding decisions, particularly when the funding for the Maine Academy of Natural Sciences was discretionary.

Several judges questioned whether Eves was in a public position, similar to a superintendent hired by a popularly elected school board, or in a private position as the head of a privately run school. The questions suggested that determination could play a role in whether LePage had a right to intervene and threaten funding.

There’s no timetable for the court to issue its judgment. If the justices tie, 3-3, the lower court ruling that dismissed the lawsuit would stand.

Eves, who attended the oral arguments, said LePage’s actions represented “an extreme abuse of power” and he would keep pressing the suit to make sure no future governor attempts to hurt someone’s private life over political disputes.

Only four of the judges attended Tuesday’s 30-minute hearing. Two others, who had been part of the panel the first time around, listened in on the hearing in their chambers and Judge William J. Kayatta Jr., who is from Maine, recused himself. Kayatta wasn’t required to say why he decided he couldn’t participate in the case.