Two losing candidates in Central African Republic's presidential race demanded on Tuesday a manual recount of ballots cast in last month's first-round vote, saying that widespread irregularities undermined the credibility of the results.

The election appears set to head to a second round after provisional results showed two ex-prime ministers - Anicet Georges Dologuele and Faustin Archange Touadera - in the lead but neither winning an outright majority.

Observers have praised the mainly peaceful nature of the December 30 polls, which many hope will help put an end to years of deadly inter-religious bloodshed.

However, Andre Kolingba and Martin Ziguele, who finished third and fourth and are both members of the Alliance of Democratic Forces for Transition (AFDT) political platform, are disputing the result.

"The AFDT demands ... an audit of the collection chain for electoral data, a manual recount of candidates' ballots, and the publication of the recount," AFDT member Nicolas Thiangaye said at a news conference attended by the two candidates.

Kolingba and Ziguele lodged complaints with the constitutional court following the announcement of the provisional results by the elections commission last week. The court is charged with certifying those results and is expected to make a ruling this week.

Central African Republic descended into turmoil in early 2013 when mainly Muslim Seleka rebels seized power in the majority Christian nation, provoking reprisals by Christian militia fighters.

Around one in five Central Africans has been displaced in the ensuing violence, leading to de facto partition along religious and ethnic lines.

"The organisation of these elections by the National Elections Authority was tarnished by dysfunction and numerous irregularities which are of a nature to discredit the results of the polls," the AFDT said in a separate statement.

Some 20 of the 30 candidates vying to lead the former French colony had previously voiced objections to the vote and urged vote counting to be halted. But most of them have since changed their position.