Kais Said and Nabil Karoui say exit polls show they have made it to runoff, with preliminary results due on Tuesday.
Two anti-establishment candidates claimed the lead in the first round of Tunisia's presidential election on Sunday, in a poll focused on high unemployment and a surge in the cost of living.
Twenty-four candidates were standing in the election, the second since longtime ruler Zine El Abidine Ben Ali was removed in the 2011 revolution.
However, in a sign of voter apathy, especially among the young, the elections commission (ISIE) reported turnout was only 45 percent, down from 64 percent recorded in the first round in 2014.
Kais Said, a 61-year-old law professor and expert on constitutional affairs who ran a low-key campaign as an independent, claimed to be in the lead for the runoff.
He finished "first in the first round", he said, citing exit polls in advance of preliminary results, which are expected to be announced on Tuesday.
There was also an upbeat atmosphere at the party headquarters of media mogul Nabil Karoui, who is behind bars being under investigation for money laundering, as hundreds of supporters celebrated after he also claimed to have reached the second round.
Candidates must secure 50 percent of the vote to win outright, but if none of the hopefuls obtains a majority the two with the most votes will advance to the decisive runoff. The date of the second and final round has not been announced, but it must happen by October 23 at the latest and may even take place on the same day as legislative polls, slated for October 6.
Tunisia's president has limited powers - in charge of foreign policy, defence and national security - and governs alongside a prime minister chosen by parliament who has authority over domestic affairs.
'Very worst up'
More than seven million people were eligible to vote, with prominent first-round candidates including Abdelfattah Mourou, heading a first-time bid for Islamist-inspired party Ennahdha, and Prime Minister Youssef Chahed.
Ennahdha insisted it would wait for the official results.
"Only the elections board gives the results," said Ennahdha MP and Mourou's campaign director, Samir Dilou.
"I do not doubt the work of the polling institutes, (but) it is not their role to impose a certain truth on the public," he told reporters.
Chahed's popularity has been tarnished by Tunisia's economic malaise.
The prime minister has also found himself having to vehemently deny accusations that Karoui's detention was politically inspired.
Initially, 26 candidates had been contesting the election, but the crowded field was narrowed slightly by the last-minute withdrawal of two candidates in favour of Defence Minister Abdelkarim Zbidi just before Saturday's campaign blackout.
Zbidi has pledged he would change Tunisia's constitution to strengthen the presidency.
Last week, Karoui, 56, launched an open-ended hunger strike but on Friday an appeal to have the Tunisian businessman released from jail was rejected, his party and lawyers said.
Some hopefuls, including Said, sought to burnish anti-establishment credentials in a bid to distance themselves from a political elite discredited by personal quarrels.
The 61-year-old law professor avoided attaching his bid to any political party, going door-to-door instead to drum up support for his conservative platform.
Leila Thabbi, a 40-year-old housewife, arrived at the polling station with her toddler.
"I am voting for the future of Tunisia for my children," Thabbi told Al Jazeera. "I am worried for Tunisia. The situation gets worse and worse, there are no opportunities, especially for my children."
Publication of opinion polls has officially been banned since July, but it is apparent the shifting political landscape had left many voters in a quandary.
ISIE head Nabil Baffoun had urged Tunisians, especially young people, to come out and vote before the polling stations closed on Sunday.
"We must leave our homes and vote - it's a right that we gained from the 2011 revolution which cost lives," Baffoun added, visibly disappointed by the turnout.
However, he later said that the turnout of 45 percent was "an acceptable level".
Distrust of the political elite has been deepened by an unemployment rate of 15 percent and a rise in the cost of living by close to 30 percent since 2016.