Partial results from the official election commission are expected to be released throughout the day today, but the Nida Tunis (Tunis Calls) party cited exit polls to say it has won more seats than any other party in the 217-member parliament.
"According to the information we have, we should have around 80 seats," said Aida Klibi, a party spokeswoman.
The election, in which 60 percent of Tunisia's 5.2 million registered voters participated, will produce the nation's first five-year parliament following the country's 2011 Arab Spring revolt and has already been widely praised around the world.
The peaceful and orderly manner in which the elections unfolded yesterday was also lauded by the European Union and France.
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If the exit polls, which give Nida Tunis 37 percent of the seats and just 26 percent to the moderate Islamist Ennahda Party are confirmed by the vote count, it would be a dramatic reversal for the Islamists, which had ruled the country for two stormy years in a coalition with two other liberal parties.
"We have a picture forming and we are not as optimistic as last night," said Yusra Ghannouchi, a spokeswoman for the party.
Created as an explicit counterbalance to the Islamists after their 2011 election victory, Nida Tunis includes businessmen, trade unionists and many politicians from the deposed dictator Zine El Abidine Ben Ali's government.
They seek to evoke the heritage of Tunisia's first post-independence president, Habib Bourguiba, with his focus on education and modernisation, while playing down the one-party state that Tunisia had been for half a century.