Robert Mueller is balking at testifying publicly before Congress, pushing for a closed-door appearance in negotiations with House Democrats, according to three people familiar with the special counsel’s position.

Robert Mueller
Photographer: Alex Wong/Getty Images

Mueller has told the Democratic-controlled House Judiciary Committee that he doesn’t want to be dragged into a political fight and that he’s hesitant to publicly discuss his final report, according to the people, who asked not to be identified discussing the continuing negotiations.

Among the options Mueller has raised is...