The turmoil has tarnished the image of ex-president Nicolas Sarkozy's UMP — still reeling from its loss of the presidency and parliament this year — and raised the spectre of a split on the right that would benefit the ruling Socialists.
Former prime minister François Fillon, 58, and ambitious UMP secretary general Jean-Francois Copé, 48, have traded accusations of fraud and bad faith since last Sunday's party vote ended with Copé ahead by a handful of votes.
Former French prime minister Alain Juppé, called in to help end the crisis, said on Sunday he had failed to resolve the fractious leadership dispute.
Juppé said in a statement that "the conditions for a mediation did not come together" during talks between the party's two rival leaders and that "therefore he considers that his mission is over".
Earlier, he frankly expressed pessimism about the chances of the talks succeeding.
"I am doing everything I can to succeed even if there is very little chance," Juppé told French media.
"If they do not accept (his conditions), I will withdraw, it's no big deal, they will sort themselves out."
A meeting of UMP officials aimed at resolving ballot disputes collapsed Sunday, with Fillon representatives walking out after about an hour.
A lawyer for the Copé camp accused them of "choosing to desert" the talks.
The meeting with Juppé marked the first time the rivals had met face-to-face since the leadership contest to replace Sarkozy, who lost to Socialist Francois Hollande in May's presidential vote, descended into chaos.
Copé was declared the winner of the leadership battle by a margin of just 98 votes in a contest in which more than 150,000 party members voted.
The party electoral commission has since said that ballots cast in France's overseas territories that were not counted would have reversed the result.
The Copé camp has claimed he would have won by a clear margin but for vote-rigging in the Mediterranean city of Nice.
The party has faced ridicule over the debacle, at a time it could be taking advantage of Hollande's falling popularity over his handling of France's struggling economy.
The party's former secretary general, ex-labour minister Xavier Bertrand, urged the UMP to clean up its act and warned its existence was at stake.
"This spectacle, this image we have put forward this week, is shameful, not worthy of a great political party," he told France 2 television.
"We must emerge from the crisis we are sinking into, I don't think that in the last 10 years the UMP has ever been in as much danger."
A source close to Sarkozy told AFP that the former president, who was in Shanghai to speak at a conference, had been in telephone contact with Juppé and was "in favour of all initiatives that could resolve the situation".
In an IFOP poll published on Sunday in Le Journal du Dimanche newspaper, 71 percent of respondents and 67 percent of UMP supporters said the leadership vote should be run again.