At least five of the 19 candidates in the race issued statements as results trickled after the election on Sunday, congratulating Faye.

However, former prime minister Amadou Ba, the ruling coalition's candidate, said that celebrations were premature.

"For our part, and considering the feedback of the results from our team of experts, we are certain that, in the worst case scenario, we will go to a run-off," Ba's campaign said.

Millions took part in a peaceful day on voting to elect Senegal's fifth president following three years of unprecedented political turbulence that sparked violent anti-government protests and buoyed support for the opposition.

At stake is the potential end of an administration led by outgoing President Macky Sall that has promoted investor-friendly policies but failed to ease economic hardship in one of coup-prone West Africa's more stable democracies.

Nineteen contenders vied to replace Sall, who is stepping down after a second term marred by unrest over the prosecution of firebrand opposition leader Ousmane Sonko and concerns he wanted to remain president past the constitutional limit.

Sall's ruling coalition picked Ba, 62, as its candidate.

About 7.3 million people were registered to vote in the country of about 18 million.

Turnout was 71 per cent, according to state television RTS.

The first set of tallies announced on television showed Faye had won the majority of votes, triggering widespread street celebrations in the capital Dakar.

At least five opposition candidates later declared Faye the winner, effectively conceding defeat.

They included one of the main contenders, Anta Babacar Ngom, who wished Faye success as leader of Senegal in a statement.

It was not clear how many of the 15,633 polling stations have been counted.

Final provisional results are expected by Tuesday.

A second round of voting will only take place if no candidate secures more than 50 per cent.

Sonko, in jail until recently, was disqualified from the race because of a defamation conviction.

He is backing Faye, the co-creator of his now dissolved Pastef party, who was also detained almost a year ago on charges including defamation and contempt of court.

An amnesty law passed this month allowed their release days before the vote.

Sall, first elected in 2012, is leaving office after a drop in popularity that deepened when authorities sought to postpone the vote to December. It was initially scheduled for February 25.

The move stoked unrest and concerns about authoritarian overreach, prompting Senegal's Constitutional Council to rule the vote should go ahead before the end of Sall's mandate on April 2.

Faye has promised to root out corruption, restore stability and prioritise economic sovereignty, appealing to the urban youth frustrated by a lack of jobs in a country where 60 per cent of people are younger than 25.

Australian Associated Press