Jean-François Copé, the party's populist secretary-general, claimed a clear win while former prime minister Francois Fillon said he believed he had edged the contest subject to confirmation by the electoral commission which oversaw the poll.
"The French people are watching us. We do not have the right to announce the result before those in charge of the vote," said Fillon in a swipe at Copé that reflected the acrimonious nature of the campaign.
Copé said: "The activists of the UMP have accorded me a majority of their votes and therefore have elected me as the president of the party."
Aides to Copé said he had won 1,000 more votes than his rival in a poll in which more than half of the UMP's 300,000 members had cast their ballots. Fillon said he was 224 votes ahead.
But the electoral commission suspended the count till 10:00 am (0900 GMT) Monday, with the chairman saying records from 50 percent of the regions were missing.
Fillon, who paid a brief visit to the scene of the count, said drily: "We note that at 0300 in the morning our political group is unable to give a result."
Both camps claimed there had been irregularities in voting in several departments and it was unclear how long it would take the electoral commission to check the voting and announce a winner. The vote came six months after Sarkozy's presidential election defeat by Socialist François Hollande.
Whoever emerges as the new UMP leader will be taking over a party well-placed to capitalise on Hollande's slump in popularity and the economic gloom engulfing the country.
But he may also face a difficult task in uniting the party after a bitter battle that delighted the UMP's rivals.
"It is obvious that whoever is elected president of the UMP will have no legitimacy whatsoever given that he will be in charge of a party broken in two," said Florian Philipott, the deputy leader of the far-right National Front.
The new leader is not certain to be the mainstream right's candidate at the next presidential election in 2017.
Sarkozy is now establishing himself on the money-spinning international conference circuit but he has not ruled out a return to national politics.
Polls suggest two thirds of UMP supporters want him to have another tilt at the presidency.
Fillon, who was prime minister for five years until Sarkozy was ousted by Hollande in May, went into the vote as the marginal favourite, hoping to sell himself as a unity candidate capable of appealing to centrist voters.
Both Fillon, 58, and Copé, ten years his junior, are seen as advocates of free market policies and economic reform. But they differ on social issues with Copé sharing Sarkozy's populist approach on immigration and the integration of Europe's largest Muslim community.
He last month published "A Manifesto for an Uninhibited Right", in which he lambasted a culture of "anti-white racism" amongst immigrant communities in impoverished urban areas.
He caused further controversy with a tweet about a boy who allegedly had his breakfast pastry (pain au chocolat) snatched from him during the Muslim fasting month of Ramadan.
Fillon accused his rival of opportunism, while seeking to portray himself as an experienced statesman - a stance that prompted Copé to dismiss him as the "Hollande of the right," in a reference to the president's perceived lack of charisma and reputation for dithering.