In the meantime Haiti has had an interim leader, Jocelerme Privert, who was chosen by the legislature
Nearly 6.2 million people were eligible to vote in the Caribbean nation, parts of which are still struggling to recover from a devastating hurricane, and long lines formed Sunday as many cast their ballots.
There were scattered reports of civil unrest and a small number of arrests, but order generally held, boosting hopes that at long last institutions may be renewed and constitutional rule returned.
But Haiti is not yet free of the fear that this year's attempt to choose a leader will end as it did in 2015, when election results were cancelled amid protests and reports of massive fraud.
Former president Michel Martelly's mandate expired after last year's cancelled poll, but his party is still keen to see his anointed successor Jovenel Moise take office.
In the meantime Haiti has had an interim leader, Jocelerme Privert, who was chosen by the legislature.
On Monday, in defiance of a declaration by the Provisional Electoral Council (CEP) that no official results of Sunday's first round vote would be known for days, Martelly's PHTK party declared a win.
According to PHTK spokesman Rudy Herivaux, apparently citing unconfirmed partial figures, not only did Moise win the first round vote but he secured more than 50 percent and avoided a run-off.
"We know this officially already," he said, declaring Moise to be Haiti's president-elect. "The country knows it. The whole world knows who is the president-elect of Haiti -- it's not a mystery."
Not to be outdone, supporters of the opposition Fanmi Lavalas -- the party of former president Jean-Bertrand Aristide -- also declared victory for their candidate Maryse Narcisse.
Hundreds of Aristide supporters poured into the streets of poor neighborhoods of Port-au-Prince, where the former exile is still a hero to many.
"We're going to stay in the street until they give us what we won at the ballot box," declared Lucher Jean-Joseph. "We voted for Maryse Narcisse and she won on the first round, there's no way past that.
"If they want a revolution, we'll give them it."
Legally, only Haiti's CEP can declare official results, and ballots from many areas of the poor and recently hurricane-swept nation have yet to be counted.
International observers are worried that aggressive moves by the players could provoke renewed unrest and undermine the credibility of the process.
UN Secretary General Ban Ki-moon welcomed the peaceful conduct of polling, but urged patience.
"The secretary general stresses that this electoral process is crucial to ending the current governance vacuum in Haiti," Ban's office said.
"He urges all actors to await the results proclaimed by the CEP and only use legal channels for any eventual challenges."
The United States, Haiti's main international donor and partner, has been frustrated by the slow pace of the electoral system and wants a clear outcome, but also offered only cautious congratulations.
US State Department spokesman John Kirby called the vote an "important step towards returning Haiti to full constitutional rule" and hailed those Haitians who voted "in a peaceful manner."
Kirby noted what he said were "isolated incidents" of intimidation and urged Haiti to deal with them under the law while preparing a second round vote if needed and a new president "in early 2017."
Moise, an agricultural baron, was declared winner last year, only to see the results cancelled after a ballot audit found evidence of large-scale fraud.
This year his party appears to be trying to go one better by eliminating the opposition candidates -- including Jude Celestin of the LAPEH party -- without the need for a second round.
Last year's second-place Celestin faced two more heavyweights -- popular leftist senator Moise Jean-Charles and Narcisse, a spokeswoman for Aristide and flag-bearer for his movement.
But Haiti must wait to find out if a split in opposition support has given Moise an early victory. The CEP is not due to report official tallies for eight days.
CEP head Leopold Berlanger warned Sunday after polls closed that partial returns cited on the group's online tally are provisional and incomplete and should not be used to predict the result.