Speaking at a press conference in Tehran on Saturday, the minister put the turnout at over 60 percent and said counting the ballots is in progress with high precision.
The initial results of the polls in the capital, Tehran, will be released on Saturday night, he noted.
According to the minister, there will be a run-off in April in the constituencies where no candidate wins a majority.
Earlier, head of the Elections Headquarters said the final results of the polls in Tehran are expected to be announced within the next three days.
Polling stations opened on Friday morning and were scheduled to close after 10 hours. But the higher-than-expected turnout convinced 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.
By Tasnim News Agency
