Francois Fillon has set up his own faction of the UMP party in the French parliament, demanding a repeat of the leadership ballot within three months.
The ex-prime minister said the faction, Rally for the UMP (R-UMP), would be dissolved if a new vote was announced.
He disputes the victory of Jean-Francois Cope, whose narrow win has been reconfirmed by party officials.
A compromise may be emerging under which the party would hold a referendum on the need for a new ballot.
Mr Fillon said he favoured the idea, floated by Mr Cope, of a party referendum in January, but stressed it must be held "in conditions of objectivity".
Of the 183 UMP deputies in the National Assembly, it is believed at least 60 will join Mr Fillon's faction.
The split was forced by a parliamentary deadline for all MPs to declare their party affiliation for next year's funds.
The ruling Socialist Party had refused to move the Friday deadline.
In practical terms, this means Mr Cope's supporters will lose crucial public funding at a time when the UMP is beset by debt, because the breakaway group will take some of the funding with them.
Parties receive an annual sum of 42,000 euros (£34,000; $54,000) per deputy.
The original ballot was held by the party on 18 November for its 300,000 or so members, and Mr Cope was announced the winner by just 98 votes.
A recount was ordered after Mr Fillon's supporters found returns for three overseas territories had been overlooked but on Monday Mr Cope's election was reconfirmed with an increased majority - nearly 1,000 votes.
"The time is not right in the heat of the moment, in the bitterness... to say we must vote again right away," Mr Cope said on France Info radio on Tuesday.
Francois Fillon is also pursuing the so-called "nuclear option" with a legal challenge to the vote, the BBC's Christian Fraser reports from Paris.
Bailiffs went twice to the offices of the UMP on Monday to secure the voting record.
Amid all the bitterness, it was always unlikely that the two camps would find a mutually acceptable agreement, our correspondent says.
On Monday, the hashtag RUMP was the top-trending term on Twitter in France with the names of both Mr Cope and Mr Fillon also in the top 10 list, as the UMP feud gripped France.
Mr Cope, who is firmly on the right wing of the UMP, had the support of many party activists during the contest.
By contrast, Mr Fillon, with his more moderate views on issues such as Muslim integration, appeared to enjoy broader appeal outside the party.
At a peacemaking lunch Monday with Mr Fillon, former President Nicolas Sarkozy said holding a new vote would "avoid an escalation of the conflict", a party source told AFP.
This account was confirmed by both Fillon and Cope loyalists in the party, the French news agency said.
The RUMP was due to hold its first meeting in parliament later on Tuesday.
Meanwhile, Mr Cope visited the Elysee Palace as leader of the UMP to discuss political reform in France with President Francois Hollande.