A leading member of Nidaa Tounes party said Sunday party candidate Beji Caid Essebsi was leading the presidential race.
Essebsi will run the second round by at least 10 percentage points, Mohsen Marzouq, head of electoral campaign of Essebsi said.
For his part, Adnan Mansour, head of electoral campaign of rival Moncef Marzouki, the incumbent president, denied such claims.
The polls closed after Tunisia's first presidential election since the 2011 Arab Spring that triggered uprisings across the region.
Essebsi served as minister of the interior, defense and foreign affairs under the country's founding president, Habib Bourguiba.
He was then parliamentary speaker under deposed former president Zine El Abidine Ben Ali, which led to critics accusing him of seeking to restore the old regime.