Iranian moderates have won a majority in parliament and a top clerical body charged with selecting the next supreme leader, dealing a major blow to hard-liners in the first elections held since last summer's landmark nuclear agreement with world powers.

Final results released by the Interior Ministry and broadcast on state TV show that reformists, who favour expanded social freedoms and engagement with the West, won at least 85 seats. Moderate conservatives, who also supported the nuclear agreement, won 73, giving the two camps a majority in the 290-seat assembly.

Hardliners, who had opposed the deal, won just 68 seats, down from more than 100 in the current parliament. Five seats will go to religious minorities, and the remaining 59 will be decided in a runoff, likely to be held in April.

Interior Minister Abdolreza Rahmani Fazli said turnout was 62 per cent.

Moderates also won a 59 per cent majority in the Assembly of Experts, an 88-member body which will choose the successor to Ayatollah Ali Khamenei, who has been Iran's top decision-maker since 1989. The 76-year-old underwent prostate surgery in 2014.

President Hassan Rouhani and former President Akbar Hashemi Rafsanjani, both considered moderates, retained their seats in the assembly, according to the Interior Ministry. However, several prominent hard-liners, including Ayatollah Ahmad Jannati, have also been re-elected.

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The election results should make the assembly less hostile to President Hassan Rouhani, as he "will face a friendly parliament" who can support his drive for economic reforms and expand social reforms. (Atta Kenare/AFP/Getty Images)

Jannati is also the leader of the Guardian Council, an unelected, constitutional watchdog that vets election candidates.

He has been a leading opponent of democratic reforms and has pressed for the disqualification of reformist candidates.

Out of 3,000 reformists who applied to run in this year's elections, just 200 made it through the vetting process.

Women's rights a focus for 'friendly parliament'

The election results should make the assembly less hostile to Rouhani, as he "will face a friendly parliament" who can support his drive for economic reforms and expand social reforms, including for women, said Ali Reza Khamesian, the campaign manager for top reformist vote-getter Mohammad Reza Aref.

"Getting parliamentary approval to lift restrictions on women attending male sports stadiums and providing greater protection for women's rights will be among the measures" Rouhani can achieve, he said.

At least 12 women have already been elected to parliament, including Fatemeh Hosseini, a 30-year old business administration expert, and six others will compete in the runoff vote. A win by three in the second round would make for the biggest female parliamentary presence in Iran's history.

"As a young woman, I ran to inspire women and give them courage to fight for their rights. I ran to play my role in the destiny of the country and stop extremists from capturing seats in parliament," Hosseini said.

The Assembly of Experts is elected every eight years. Moderates previously held around 20 seats in the assembly.