Tunisia's secularists are poised to win the most seats in a close-run election that should see the country's ruling Islamists pushed into second place.
The Nidaa Tounes party is expected to win around 80 of 217 seats, with the governing Ennahda party taking 70.
Ennahda officials have congratulated Nidaa Tounes and urged them to form an inclusive government.
Tunisia's transition to democratic rule after a 2011 revolt has been hailed as a regional success story.
The revolt was the first and least violent of the Arab Spring uprisings against autocratic governments across the region.
The parliamentary poll was the second such election since the uprising.
Ennahda official Lotfi Zitoun told Reuters news agency his party accepted the result and congratulated the winner.
"We are calling once again for the formation of a unity government in the interest of the country," he was quoted as saying.
Earlier, Ennahda leader Rachid Ghannouchi was quoted as saying that the winner of the election should respect Tunisia's need for "a government of national unity, a political consensus".
"This is the policy that has saved the country from what other Arab Spring countries are going through," he told local TV station Hannibal.
At the scene: The BBC's Naveena Kottoor in Tunis
At the Nidaa Tounes party headquarters the reaction this afternoon to the lead in the polls was still restrained. "This is a victory for Tunisia," they told the BBC. While the party was widely expected to do well, the top spot still comes as a surprise not only to the party, but to many Tunisians.
Nidaa Tounes emerged on the political scene in 2013. It is a hotchpotch of independents, secular politicians and - to the dismay of many - former regime officials who served under deposed President Zine al-Abidine Ben Ali.
The party has strong support among the public administration and the Tunisian elites, many of whom still enjoy the same privileges they enjoyed under the previous regime.
Its octogenarian leader, Beji Caid Essebsi, is also a leading candidate in the upcoming presidential polls. His strategy has been to focus on his extensive experience compared to his rivals.
For Ennahda and the two smaller secular parties that formed the first elected government here after the revolution, the election result is a bitter pill to swallow. Many were proud of their role in writing and adopting a new constitution. But it seems that the electorate has punished them for the lack of economic and social reform.
"This result is fine, I am not really surprised," one member of Ennahda's political bureau told the BBC. "Governments that are leading during a political transition are often punished at the polls."
Talks on a possible power-sharing deal are expected to begin this week.
Tunisia's secularists and Islamists have managed the transition to democracy with less acrimony and bloodshed than their neighbours, correspondents say.
The country nevertheless faces a persistent low-level threat from militants.
Radical groups had threatened to disrupt the elections, and on Thursday, gunmen shot a policeman on the outskirts of the capital, Tunis.
But voting on Sunday appeared to pass without any major incidents.
Around five million Tunisians were registered to cast their ballot, with overseas residents having already voted on Friday.