Three weeks after his opponent Jean-François Copé was declared the winner in a leadership vote, former French prime minister François Fillon proposed on Tuesday to hold a new primary among right-wing voters — one in which he might not stand for election.

Fillon refused to concede defeat in November’s primary election, claiming that votes from France’s overseas territories had been “forgotten” in the count. An electoral committee for the conservative Union pour un mouvement populaire invalidated the results from New Caledonia in the Pacific and two voting stations in Alpes-Maritimes in the southeast of the country where it claimed there had been fraud. The committee finally put Copé ahead by 952 votes.

Fillon, who served as President Nicolas Sarkozy’s prime minister for five years and is considered more centrist, immediately announced that “the only worthwhile solution is a revote” and split the conservative delegation in parliament between his supporters and Copé’s. The latter took that as the crossing of a “red line” and rejected another election. A compromise proposal to organize a referendum on whether or not to call another vote was dismissed by both candidates.

The former premier reiterated his call for a revote on French radio on Tuesday. “If we are talking about a revote before the summer, with a reform of the statutes and fully opening the game to new candidates to ensure a reoxygenation of our party, then I am in favor,” he said.

In a veiled challenge to Copé, Fillon added that he would “probably not” stand in a primary election again. “My ambition is to rally the French around a plan for national recovery but not necessarily as leader,” he insisted. “I am not fighting for me.”

Copé, who served as the party’s secretary general for two years before he ran for its leadership, has repeatedly said that he doesn’t want to call another vote until after the 2014 local elections.

The infighting on the French right is as much about personalities as it is about its future electoral strategy. Copé, a hardliner and protégé of Sarkozy’s, has promised to stand aside if the former president decided to run again in 2017. Fillon has made no such promise but may be a more viable general election candidate as he can appeal to the center whereas Copé would likely draw votes from the far right.

A vast majority of French conservatives, if not a majority of French voters, would by now rather Sarkozy returned to the presidency than either of his possible successors. Their popularity, especially Copé’s, has plummeted. According to an opinion poll published in Figaro Magazine late last month, 70 percent of French conservatives supported Fillon, down from 81 percent in October. 44 percent approved of Copé, down from 64 percent before the primary.

Among the general electorate, Fillon enjoyed the sympathy of 38 percent of voters, down from 44 percent a month before. Just one in five voters still saw a role for Copé in national politics, down from 27 percent in October.