Both candidates, Jean-Francois Cope and Francois Fillon, have claimed victory and accused their rival of fraud and ballot-stuffing.
Only a handful of votes separate right-wing candidate Jean-Francois Cope and ex-Prime Minister Francois Fillon.
A final result is expected later on Monday, but party grandees said the UMP had been damaged, and urged both candidates to end their war or words.
“The movement has emerged divided and thus weakened by this excessive confrontation,” wrote the former prime minister and foreign minister, Alain Juppe, in his blog.
“Throughout the campaign, it has been less a question of the future of the UMP and more about the two candidates’ obsession with 2017 the date of the next presidential election.
“We have to get out of this lamentable situation to avoid the implosion of our party.”
Alain Juppe called on both Jean-Francois Cope, the party’s secretary general since 2010 and Francois Fillon, prime minister under Nicolas Sarkozy, to “accept the decision of the electoral commission when it is delivered”.
When initial results emerged late on Sunday, Jean-Francois Cope was narrowly in the lead, surprising political pundits who had expected the former prime minister to win. Opinion polls had consistently given Francois Fillon the edge.
The contest has been bitterly fought throughout by the two rivals and, even before the result came through in the southern coastal city of Nice, Jean-Francois Cope’s team complained of fraud and demanded an investigation.
A UMP deputy mayor backing Jean-Francois Cope said that there had been “a certain number of irregularities” in polling stations in the Alpes-Maritimes area. In one polling station in Paris, a party official complained that there were 40 more ballots than voters on the party list.
Francois Fillon’s team also registered a complaint.
The leading conservative daily newspaper, Le Figaro, called the election an open crisis and French political analysts say the immediate beneficiary of the vote could be the far-right National Front, whose candidate, Marine Le Pen, polled third in the presidential election in April.
The UMP was only created 10 years ago by President Jacques Chirac to unite the diverse wings of the French right.
The party was very much his personal fiefdom until he retired from politics in 2007 and was succeeded by Nicolas Sarkozy.
The two candidates have different visions for the party.
Jean-Francois Cope is considered more right wing. Last month he produced “A Manifesto for an Uninhibited Right” in which he claimed that gangs in the city suburbs were fostering “anti-white racism”.
Francois Fillon is seen as sober and more restrained.
The winner will inherit a party in difficult financial straits, after a series of electoral setbacks over the past five years, culminating in Nicolas Sarkozy’s presidential defeat to Socialist rival Francois Hollande.
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