Saied, a conservative, won the presidential election earlier this month. He succeeds the late Beji Caid Essebsi, who died in office in July.
Tunisians are going to choose the president among a populist tycoon who just got out of jail against a conservative professor in a runoff vote on Sunday.
Ennahda came first in Sunday's parliamentary election, winning 52 seats, while media mogul Nabil Karoui's Heart of Tunisia party won 38 seats in the 217-seat chamber, the electoral commission said.
While preliminary official results are not expected until Wednesday, Ennahdha and Qalb Tounes (Heart of Tunisia) — who have ruled out forming an alliance— were both swift to claim victory.
The vote comes two weeks after the first round of a presidential election that swept aside traditional political parties in favour of independent candidates, a trend likely to be repeated in the ballot for MPs.
During his era, Ben Ali's photograph was displayed in every shop, school and government office from the beach resorts of the Mediterranean coast to the impoverished villages and mining towns of Tunisia's hilly interior.
Neither candidate has ever held political office but they beat out two prime ministers and the candidate for the moderate religious party Ennahdha.
Tunisia is the only Arab country to have emerged with a viable civil society and democracy after the Arab Spring, but the system is on the ropes as authoritarianism casts its shadow over the country.
Nothing is certain in Tunisia's presidential election, only the second since the 'Arab Spring'.
As the election campaign gains momentum, the country's media tycoon Nabil Karoui remains imprisoned in a highly politicised case, raising questions about the judiciary's non-interference in court cases.
Tunisian Prime Minister Youssef Chahed's supporters set up a new political party to compete for the next presidential and parliamentary elections in late 2019. Could it be a game changer?
Prominent Tunisian politician Moncef Marzouki blames the UAE for interfering in Tunisian politics and trying to topple the democratically elected Tunisian government.
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