RALEIGH, N.C. — A federal appeals court on Tuesday questioned whether a lower court got it right when it blocked a challenge to Representative Madison Cawthorn’s candidacy by voters who cited a section of the Constitution addressing insurrection as disqualifying him.

Three judges on the 4th U.S. Circuit Court of Appeals in Richmond, Virginia, heard arguments in a lawsuit that the first-term Republican congressman filed to derail the formal challenge sent to the State Board of Elections from going forward.

U.S. District Judge Richard Myers ruled for Mr. Cawthorn in March and prevented the board from formally examining whether he should remain on ballots, and the voters appealed. Mr. Cawthorn is one of eight candidates on the May 17 primary ballot for the 11th Congressional District. There’s no timetable on when the judicial panel will rule, but the court did accelerate the appeal process.

The challenge focused on Mr. Cawthorn’s involvement in the rally that preceded the Capitol riot in January 2021 at which the presidential election outcome was questioned. The voters cite Section 3 of the 14th Amendment ratified in 1868 that is designed to prevent congressmen who had fought on the Confederate side during the Civil War from returning to Congress.

Similar challenges have been filed against members of Congress in other states who have been strong supporters of President Trump, including Representative Marjorie Taylor Greene. A Georgia state judge recently heard testimony from Ms. Greene but has yet to issue a finding. They will be passed on to Secretary of State Brad Raffensperger, who will ultimately determine whether Ms. Greene is qualified.

Some circuit judges Tuesday raised doubts about Judge Myers’s logic and those of Mr. Cawthorn’s attorney, who said an 1872 law that removed office-holding disqualifications from most ex-Confederates also exempt current members of Congress like Mr. Cawthorn today.

“Why would Congress do this anyway?” U.S. Circuit Judge Jim Wynn, a nominee of President Obama, asked during oral arguments. “Why would you rather take away a disability of an individual who’s going against the United States?”

The amendment says no one can serve in Congress “who, having previously taken an oath, as a member of Congress … to support the Constitution of the United States, shall have engaged in insurrection or rebellion against the same.” The amendment does allow Congress to pass laws that can remove such restrictions.

But any such law can’t for all time prevent prohibitions against future insurrectionists, a Raleigh attorney representing voters who filed formal challenges of Mr. Cawthorn, Press Millen, said.

“You cannot simply amend the Constitution through a vote in Congress,” Mr. Millen said. A federal judge in Georgia last month said she disagreed with Judge Myers and ruled the 1872 Amnesty Act didn’t apply to Ms. Greene.

James Bopp, Mr. Cawthorn’s lawyer, said his client “vigorous denies that he ever engaged in insurrection or rebellion against the United States, the country he loves. But this is not about the facts. This is about the law. This is about whether there are valid claims that are being made under Section 3 against him.”

Mr. Bopp, who also represents Ms. Greene in her case, told the judges that the Constitution leaves the decision on whether someone is disqualified to serve in the House of Representatives with the elected body itself, not the states. That means a candidate’s ultimate seating doesn’t get settled until when each two-year session begins in January, he said. In the meantime, Mr. Bopp suggested, elections will work out potential conflict.

“In a democracy … where we have the right to vote and we have the First Amendment, we leave a lot of things to the voters,” Mr. Bopp said. Mr. Millen countered by saying the Constitution makes clear that insurrectionists can’t be members of Congress, just like teenagers or citizens of other countries.

The tangled case began in January, when candidate challenges were initially brought against Mr. Cawthorn by voters in a district that he initially decided to run in this fall. But North Carolina’s congressional map for the 2022 elections was altered twice since then because of redistricting litigation that changed the district that Mr. Cawthorn decided to run in this fall. That led to a second challenge by voters in the 11th Congressional District.

Judge Myers refused to let voters from the new 11th District and the other district that Mr. Cawthorn had officially filed to run in earlier formally enter the lawsuit. Those denials also form part of the appeal argued Tuesday and also were heard by Circuit Judges Julius Richardson and Toby Heytens. Judge Richardson was a Trump nominee, while Judge Heytens was picked by President Biden.