Hossein-Ali Amiri told reporters in Tehran that the figure will go up as more ballots are being counted.
Out of around 52,000 ballot boxes, more than 40,000 have been examined, he added.
The process of counting the ballots in Tehran is still in progress, and a run-off will need to be held in some major cities, Amiri noted.
In the meanwhile, the Election Headquarters issued a statement in the early hours of Saturday, calling on the whole media outlets and news agencies to refer only to the headquarters’ statements for any official figure or early results.
Polling stations opened on Friday morning and were scheduled to close after 10 hours. But the higher-than-expected turnout in the elections was enough to convince the Interior Ministry to extend the voting time three times.
Some 55 million Iranians were eligible to cast their ballots at around 53,000 polling stations across the country.
4,844 and 161 candidates have been running for the parliament and the Assembly of Experts, respectively.
There are 290 seats in the Iranian parliament, elected by direct vote of people in nationwide election for four years.
The Assembly of Experts is also a high-ranking body that elects and oversees the activities of the leader of the Islamic Revolution.
Members of the 88-seat assembly are directly elected to office by people for an eight-year term. It holds biannual meetings to appoint a new chairman.