Almost 60 per cent of eligible voters of the country's 5.2 million registered voters turned, according to the "Isie" elections commission, a significantly higher figure than the 50-per-cent turnout recorded in 2011.
The moderate Islamist Ennahda (Renaissance) - which headed the 2011 parliamentary election - and the secular Nidaa Tounes (Tunisia's Call) are thought to be the two front-running parties,DPA reported.
But according to Reuters, Nidaa Tounes has won more than 80 seats in an election for the new 217-member parliament against 67 seats for Islamist party Ennahda, a party source, citing a preliminary ballot count, said on Monday.
Election authorities are expected to announce official results later in the day, but if confirmed the result would be a setback for Ennahda, which led a government after winning the most seats in 2011 in the first free election after the fall of Zine el-Abidine Ben Ali.
Nidaa Tounes is led by former prime minister Beji Caid Essibsi, while moderate Islamist intellectual Rachid Ghannouchi heads Ennahda.A number of smaller secular parties, several of which have been open to cooperating with Ennahda, are also likely to win seats.
Essibsi said shortly after the polls were closed that there were "positive indicators" from balloting for his party.The electoral commission is due to announce preliminary results by Thursday, with final results due by November 24.
Monitors and journalists were present in force during the voting, while large numbers of police and troops were deployed to secure the elections against militants. No major incident of violence was reported.
Tunisian Islamist Ennahda Party leader and founder Rached Ghannouchi (C) gestures as he gives a speech during a campaign rally ahead of the country's parliamentary elections.
Ghannouchi, casting his vote in the northern coastal town of Ben Arous, said that the Tunisians "are a civilized people who deserve democracy.
"The elections will move the country from a fight for freedom to a fight to bring about development, eradicate poverty, and promote the economy, education, culture and the media," the Islamist leader said, in comments reported by the official TAP news agency.
There were long queues outside the polling stations in the middle class Tunis districts of LaFayette and Bardo. In the capital's working class al-Khadra suburb, a line of Ennahda supporters queued outside the polling station, DPA reports.
Some 13,000 contenders from nearly 90 political parties vied for the 217 seats up for grabs.The new parliament will have significant powers under a constitution adopted earlier this year.
Tunisia, the birthplace of the 2011 Arab Spring revolts, is due to hold a presidential vote on November 23.The parliamentary and presidential elections are intended to complete the country's process of democratization.
They are being keenly watched across the Arab world, as the country is widely seen as the sole success story of the Arab Spring uprisings.Tunisia's Islamists have taken a more cautious approach than Egypt's Muslim Brotherhood, initially forming a coalition with two centrist parties.
In January, the Tunisian Islamists withdrew from power in favour of a technocratic government as anger mounted about the 2013 assassinations of two leftist leaders by suspected “Islamist extremists”.
Ennahda says it will not run a candidate in the presidential election.
Tunisian authorities had stepped up security in the run-up to Sunday's vote for fear of attacks by terrorist, who have repeatedly clashed with police in recent months.
Both parliament and president will serve five-year terms.