Former president Nicolas Sarkozy emerged from his election defeat to issue the ultimatum to his ally Jean-Francois Copé — the twice-declared winner of last month's UMP vote — and his former prime minister, François Fillon.
If the two men do not come to an agreement on a fresh vote by Tuesday, "I will say that you both are disqualified to lead," sources close to Sarkozy quoted him as saying.
"All this has gone on for too long," he said of the worst crisis in the French right in half a century.
Sarkozy's entourage said he was "infuriated" by the deadlock after the November 18th UMP election.
Fillon's supporters have formed a breakaway parliamentary faction in the party, a decade-old coalition of Gaullist conservatives, centrists, Christian democrats and liberals.
Copé, the declared winner of the leadership vote who has refused calls for a new election, had proposed holding a referendum in December or January on whether a new vote should be held, insisting he would remain party leader until then.
But now the issue is a fresh leadership vote.
Fillon, who has threatened pursuing legal action including a civil suit to have the results overturned, signalled he may be softening his stance, saying he was ready to meet Copé's representatives as early as Monday.
"Eighty percent of our well-wishers want a new vote," he said, adding that these calls were "getting more and more pressing".
"Let us get to work from tomorrow," he said.
Copé also appeared to be backing down in the wake of his mentor's deadline, with his close ally Luc Chatel voicing support for a new election.
Although Sarkozy has no official post in the UMP after his defeat in the May presidential election to Socialist François Hollande, he is anxious to keep the UMP together in case he decides to make a comeback bid for the presidency in 2017.
Sarkozy is currently the only unifying voice who can salvage the party and wields influence over both Copé and Fillon.
Chatel told the Journal du Dimanche that the time had come "to hand over the issue to party members," adding that he backed Sarkozy's initiatives "100 percent".
Chatel said he favoured "the immediate setting up of a working group… to organize a new vote," which should be "the fruit of the work of teams from the two sides".
The UMP, the political heir to the movement founded by Charles de Gaulle after World War II, has been on the verge of collapse over the dispute, which saw the leadership vote tarnished by accusations of vote-rigging.
Fillon has formed a new parliamentary wing to break away from the UMP, depriving the party of credibility and crucial public funding.
A party appeals commission last Monday confirmed Copé's win in the leadership vote, raising his margin of victory from 98 votes to nearly 1,000 following an examination of complaints over alleged irregularities.
Fillon's Rally for the UMP (R-UMP) has attracted at least 72 of the UMP's 194 members and associate members in the National Assembly — costing the party some of the 42,000 euros ($54,000) per member it receives in public funds every year.