The vote to elect a new parliament is seen as a test run for President Macky Sall ahead of a 2019 presidential election and follows a campaign marred by violence.
The first results are due early today in the west African nation, where more than 6.2 million people are registered to vote.
There were hours-long delays to voting in several places yesterday, and some voters complained of being left off the electoral rolls.
"I'm going home. I've checked at several polling stations and my name doesn't figure anywhere. However I normally vote here," complained Souleye Tine in Dakar's working-class Medina neighbourhood.
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"Macky Sall arranged it -- he gave instructions so that in all the places where he thinks the opposition is going to win, there's no voting," Wade said.
"An election in which one of the candidates cannot find his ballot papers in the polling stations cannot be called an election," Wade said in reference to delays due to the absence of ballot papers for several electoral lists.
"I call on all voters who have voted to stay at their polling stations until the results are announced, to witness whether the results conform to reality."
Sall, in power since 2012, is seeking to bolster his parliamentary majority as he eyes a second term.
Polling stations were due to close at 6:00 pm (1800 GMT) but in the central city of Touba the governor said people could vote until midnight after particularly long delays worsened by heavy overnight storms.
A polling station in the city was vandalised by voters angry that ballot papers for Wade's coalition were unavailable, official news agency APS reported.
Sall's other main opponent, Dakar Mayor Khalifa Sall -- no relation of the president -- is in jail awaiting trial for what supporters say are politically motivated embezzlement charges.
The mayor had been seen as a key contender for 2019 and a potential threat to the president in parliament until he was charged in March with allegedly misappropriating 1.83 billion CFA francs (USD 2.85 million, 2.7 million euros) in city funds.
Wade had accused the government during the campaign of seeking to prevent an opposition victory through selective delivery of the biometric ID cards needed to vote, with several hundred thousand failing to arrive on time.
Sall said he hoped the problems with the vote would be resolved.
"I hope people will vote calmly and return home calmly," APS quoted him as saying, adding: "Senegal is a democracy that cannot be pushed backwards."
The election has been complicated by the record 47 lists of candidates in the running, meaning 47 types of ballot paper needed to be available at polling stations.
Wade has accused Sall of "destroying" Senegal, while the president's side say Wade did not do enough to develop the nation while in power, boasting of their achievements in building a new airport and other infrastructure projects.