Reformist candidates seemed poised to make major gains in two key Iranian institutions Saturday, as initial returns showed that the country had turned its back on some of the more hardline candidates in national elections.

The reformers, who are linked to President Hassan Rowhani, were taking the lead in many races as vote counting continued Saturday, including in the politically critical district of the capital, Tehran.

Interior Ministry data showed that reform candidate Mohammed Reza Aref had a commanding lead over hardliner Gholam Ali Hadad Adel. As for the rest of Tehran's seats in parliament, data showed that reform candidates were poised to take 29 of them.

More than 4,800 candidates were running for 290 seats in parliament.

Meanwhile, two reformist candidates are in the lead for the influential Assembly of Experts, the Interior Ministry said Saturday.

President Hassan Rowhani and former president Ali Akbar Hashemi Rafsanjani were placed to be in the top two positions for the 16 clerics in Tehran vying for the Assembly of Experts, which will one day decide on the next supreme leader, the de facto head of state.

The top three hardliners - Ayatollah Ahmad Jannati, Mohammed Jasdi and Mesbah Jasdi - were in 10th, 12th and 16th place, respectively, for a seat in the most important religious authority in the country.

The more votes a candidate gets, the more influence that person is likely to wield within the assembly.

While the 88-member assembly does not get involved with day-to-day political topics, wins by Rowhani and Rafsanjani would greatly reduce the influence of the ultra-conservative clergy.

Overall, the results will show whether a majority of Iranians are for or against their reformist president after he brought the country to the point where it could sign a deal with the West to lift sanctions against it, in exchange for limiting Iran's nuclear programme.

Although the nuclear programme is a source of pride in Iran, many are also chafing against the economic restrictions that have come after years of sanctions.

Without directly mentioning the results, Rowhani thanked Iranians Saturday.

"I greet you and bow down before you with respect," he said, thanking people for the credit and influence their actions have given him.

The elections on Friday for parliament and the Assembly of Experts were the first since Iran signed the nuclear agreement in July 2015, ending its international isolation.

Turnout was about 60 per cent, with some 33 million of 55 million eligible voters having taken part in the polls, according to the Interior Ministry.

The government's goal was to ensure turnout of 70 per cent. But Rowhani said on Saturday that he was pleased with the high level of participation. "The interest was so great that voting had to be extended until midnight," he said.

Interior Ministry spokesman Hussein-Ali Amiri said earlier that some cities would have to conduct run-off votes because no single candidate had reached the minimum threshold of 25-per-cent support.

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