Opposition leader Basserou Diomaye Faye is leading the race in Senegal's presidential election, local media reported.
Many of the 17 candidates have conceded to him, but the official results have not yet been announced.
Millions took part in a peaceful vote on Sunday, after three years of unrest and opposition protests against current President Macky Sall.
Amadou Ba, who was chosen by the ruling coalition, denied losing.
He said he expected a runoff to determine the winner. This will be required if no candidate receives more than 50% of the votes.
Faye, 44, a senior official in Ousmane Sonko's Pastif party, was in prison until ten days before the vote. Sonko was excluded from the race due to his defamation conviction, which he said was politically motivated.
The first set of counts announced on television showed that Faye had won a majority of votes, leading to widespread celebrations in the streets of the capital, Dakar.
Fans set off fireworks, waved Senegalese flags and blew vuvuzela horns.
The results led to five opposition candidates declaring Mr Fay the winner. Anta Babakar Nujoom, the only candidate, wished Mr Faye success in a statement.
Mr. Fay has not yet commented.
The results announced are from local media that compiles results published outside individual polling stations.
It is not clear how many polling stations have been counted so far out of 15,633 polling stations. Official results are expected by Tuesday.
He supported Sonko Faye, co-founder of the now-defunct Pastev party, who was also arrested nearly a year ago on charges including defamation and contempt of court.
An amnesty law passed this month allowed them to be released days before the vote.
They campaigned together under the slogan “Diomaye is Sonko”. Some prominent politicians and opposition candidates have supported Fay's candidacy.
“Residents are choosing between continuity and estrangement,” Fay said after casting his vote, urging the contenders to accept the winner.
Mr Sall, the incumbent, was not on the ballot for the first time in Senegal's history. His ruling coalition chose Ba, 62, a former prime minister.
“Given our panel of experts’ comments on the results, we are confident that, in a worst-case scenario, we will go to a runoff,” Ba’s campaign said.
About 7.3 million people have registered to vote in the country, which has a population of about 18 million.
The elections were scheduled to be held last month but were postponed, sparking bloody protests from the opposition.
More on Senegal's elections:
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