The voting comes amid concerns that a January 14 deadline for the new charter's adoption may not be met because of disruptions and the slow pace of deliberations.
It was on January 14, 2011, that ousted dictator Zine El Abidine Ben Ali and his family fled the country for exile in Saudi Arabia.
The National Constituent Assembly adopted Article 1 of the draft constitution, establishing the country as a republic and Islam as its religion but rejecting amendments that the Koran be the main source of law.
The article, a compromise between the Islamist Ennahda party, which heads the outgoing coalition government, and the secular opposition, was adopted by 146 votes out of the 149 ballots cast.
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Lawmakers rejected two amendments, one proposing Islam and the second proposing the Koran as "the principal source of legislation".
Mohamed Hamdi of the small "Current of Love" party defended Islamic law, saying it would give "spiritual backing to all rights and liberties".
The assembly also adopted Article 2 -- which again cannot be amended -- on the establishment of a "civil state based on citizenship, the will of the people and the rule of law".
Approving the new constitution would be a crucial democratic milestone.
Its adoption would end months of political crisis and further distance Tunisia from the chronic instability plaguing other countries in a region rocked by regime change.
Friday's first session resulted in lawmakers approving the title of the charter, by 175 votes out of the 184 MPs present, and the first three paragraphs of the preamble.