The conservative Coalition for Family initiated a referendum that called on Romanians to cast a ballot on whether they supported a constitutional amendment that would make it harder to legalise same-sex marriage.
They were backed by the influential Romanian Orthodox Church.
The south eastern European country's two-day vote requires a 30 per cent turnout to be valid.
The country's Central Electoral Bureau said 5.72 per cent of voters had cast a ballot on Saturday.
The proposed amendment would change the definition of family in Romania's Constitution to make marriage a union between a man and a woman instead of between "spouses".
Same-sex marriage is already illegal in Romania and the country does not recognise civil unions. While the referendum will not change that, it could potentially clarify the language in the constitution.
Article 48 states that the family "is founded on the freely consented marriage of the spouses". A Yes vote would change that to "marriage between a man and a woman".
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