Ibrahim Boubakar Keita has the support of the army and religious leaders
Sunday's polling was seen as a first step toward Mali's recovery from a year-and-a-half of unrest.
On Tuesday, territorial administration minister Colonel Moussa Sinko Coulibaly said partial results indicated that front-runner and former prime minister Ibrahim Boubacar Keita had a comfortable lead and could win an outright victory.
He did not reveal the extent of the margin but said if it was maintained, there would be no need for a runoff vote.
The other two top candidates are former prime minister Modibo Sidibe and a relative unknown, Dramane Dembele, who is backed by Mali's largest political party, ADEMA.
News reports on Wednesday said some candidates have rejected election projections that could give Keita an outright win.
Sunday's election was peaceful and had a relatively high voter turnout, with some areas reporting it at more than 50 percent.
The voting has come on the heels of this year's French-led military intervention, which followed a military coup and an Islamist takeover in Mali's north.
Members of the FDR coalition have claimed that world powers led by France, which pushed for the vote to be held despite concerns over Mali's readiness, favoured Keita in the process.
Cisse said he would challenge the results if Keita is announced winner in one round.
"It is up to Mr Cisse to prove what he claims and to use the legal existing channels for his claim. The imperfections will affect the winners as well as the losers," Louis Michel, the European Union's chief observer to the Mali mission, said on Tuesday.
Average turnout was tallied so far at 53.3 percent, well above Mali's record high of 40 percent, Coulibaly said. Final results could be ready on Wednesday.
Whoever wins the election will have to push through national reconciliation efforts and conclude peace talks with Tuareg separatist rebels who allowed the vote to take place but are still armed in remote corners of Mali's desert north.
They will also oversee a $3.98bn plan proposed by donors to rebuild the nation and kick-start the economy.
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