Senegal's presidential election was free and fair, observers from regional body the Economic Community Of West African States (Ecowas) have said.
The 81-year-old incumbent is seeking a second term in office
Supporters of the incumbent, Abdoulaye Wade, have been celebrating, claiming he has won Sunday's poll.
But none of his 14 opponents have conceded and predict a run-off.
A BBC correspondent says it is perhaps a sign of Senegal's stability that amid contrasting claims there has been no obvious increase in tension.
Senegal's independent electoral commission said partial official results might not be available until Wednesday.
President Wade needs to gain more than 50% of the vote to avoid a second round.
The BBC's Will Ross in the capital, Dakar, says unofficial results being telephoned in to radio stations from across the country give Mr Wade a clear lead.
Wade's opponents may team up against him if there is a run-off
But he says it is too early to know whether he has won outright in a first vote.
The Ecowas statement, while giving the vote the thumbs up, noted that there had been some problems with the process.
However, it also congratulated the Senegalese for their conduct during Sunday's voting.
Voter turnout was high and long queues left some polling stations open late.
Prime Minister Macky Sall - who is Mr Wade's campaign manager - said partial results gave the president 57% of the votes counted so far
"I invite all the other candidates to accept the voters' verdict," he said, AFP news agency reports.
Our correspondent says a run-off would present an opportunity for Mr Wade's opponents to team up against him.
That is exactly how the 81-year-old president came to power seven years ago in one of Africa's rare peaceful transitions from one president to a rival.
Mr Wade, who is seeking a second term, has come under pressure in recent months over high rural unemployment.
Since his election he has fallen out with several of his allies, some of whom were among the opponents challenging him on the ballot papers.
Two of them were Moustapha Niasse and the youthful Idrissa Seck, who have both served as prime minister in Mr Wade's administration.
Ousmane Tanor Dieng, who served under the previous president, Abdou Diouf, was also seen as a strong contender.
Senegal, a predominately Muslim nation, is seen as a rare model of stable democracy in Africa.
It is the only West African nation not to have experienced a coup since independence, and polls in 2000 passed off peacefully.
Some five million people were eligible to vote, which is almost double the figure in the last election.