Violence broke out in some of Port-au-Prince's poorest neighborhoods, which were carried by Maryse Narcisse's Fanmi Lavalas party, against Moise, the man former president Michel Martelly chose to represent his party.
Police launched tear gas grenades to disperse a crowd of hundreds of her supporters who called the vote an "electoral coup" and reacted to the advancing officers by throwing stones.
"We didn't vote in secret. All of the working-class neighborhoods in the country... Voted for Maryse, but the results they announced were an electoral coup," said Rose-Marie Rosilus.
"We will stay out in the streets until the electoral council gives us our true results," added Rosilus, who brought lemons to alleviate the effect of the tear gas.
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There were no reports of violence elsewhere in the capital or across the country.
Moise, a 48-year-old political novice and entrepreneur who worked in agriculture mostly growing bananas, earning him the nickname "banana man," wants to lift the Caribbean country out of poverty by reviving its agricultural sector.
But his rivals' challenges over the vote's legitimacy could run those plans into the ground.
The preliminary results showed that Moise won the election outright, garnering 55.7 percent of the vote, thus barring the need for a second round. But he lacks much popularity, with only 21 percent of eligible voters casting their ballots.
"We are saying there was cheating and we will see who cheated," Celestin told AFP, without naming Moise directly.
Indicating he would pursue the matter in the courts, Celestin claimed the results "do not reflect the popular vote."
But election observers from the Organization of American States said the results were "in line" with data they collected at polling stations.