Reformist allies of Hassan Rouhani won all 30 parliamentary seats in the Iranian capital, handing the moderate president a major boost on Sunday in elections seen as vital to his government.

The List of Hope, a pro-Rouhani coalition of moderates and reformists, was on course to wipe out its conservative rivals in Tehran with 90 percent of ballots counted from Friday's vote.

The clean sweep was a major fillip for the president, signalling overwhelming public backing in the capital for his landmark nuclear deal with world powers last year that ended a 13-year standoff.

The rout was completed when state television said the head of the conservative list, Gholam-Ali Hadad Adel, a former parliament speaker, was lagging in 31st place and set to lose his seat.

The landslide in Tehran came after mixed results for the president's supporters in the provinces in the first elections since sanctions were lifted last month under the nuclear agreement.

Preliminary results from a second election that took place Friday, for the powerful Assembly of Experts, which monitors the work of Iran's supreme leader Ayatollah Ali Khamenei, were also heading Rouhani's way, and could see top conservative clerics eliminated.

If the Tehran numbers are confirmed, it will seal a stunning comeback for reformists, long sidelined after the disputed re-election in 2009 of hardline president Mahmoud Ahmadinejad which was followed by bloody street protests.

Reformists said that ballot was rigged and their two defeated candidates, Mir Hossein Mousavi and Mehdi Karroubi, have been held under house arrest since 2011.

The president joined forces with reformists to try to curtail the conservatives' stranglehold on parliament and clear the way for the passage of political and social reforms.

The head of the pro-Rouhani coalition, Mohammad Reza Aref, a former vice president, was in first place in voting in Tehran, with 1.3 million votes.

The outspoken Ali Motahari, a conservative MP who switched sides and joined the slate headed by Aref, was in second spot with 1.2 million votes.

Outside Tehran, where 108 seats out of 260 have been declared so far, 33 went to the main conservative list and 24 to the reformist List of Hope.

A further 28 seats went to independents -- of whom 13 are known to lean towards conservatives and 11 are closer to reformists, with four of no clear affiliation.

None of the remaining 23 seats had a clear winner, meaning a second round of voting will be needed, which is not expected until April or May.

Turnout in the election was solid at 60 percent, but slightly less than the 64 percent of 2012.

Conservatives were also experiencing setbacks in the election to the Assembly of Experts, an 88-member group of clerics that would pick Khamenei's successor if he dies in the next eight years.

Two of three ayatollahs that the pro-Rouhani list had urged voters to reject -- Ahmad Jannati, Mohammad Yazdi and and Mohammad Taghi Mesbah-Yazdi -- were set to lose their seats.

Only Jannati, who chairs the conservative-dominated Guardian Council which must confirm the results of both elections, was safe, though he was well down the field in 15th place.

Some 16 places are reserved for Tehran, with Yazdi, the current chair of the assembly, in 17th position and Mesbah-Yazdi, a figure famously hostile to reformists, lying 19th.

Rouhani and his close ally Ayatollah Akbar Hashemi Rafsanjani, a former two-term president, held third and first places.

Even after all votes are counted by interior ministry officials, the Guardian Council's verification is not expected for several days.

Khamenei was among the first to vote on Friday and he urged the entire electorate to follow suit, saying casting a ballot is "both a duty and a right".

Many moderate voters stayed away in the last parliamentary election in 2012 in protest at Ahmadinejad's re-election three years earlier. But the Tehran landslide for the List of Hope suggested they turned out heavily on Friday.

Known as the "diplomat sheikh" because of his clerical credentials and willingness to negotiate, Rouhani delivered the nuclear deal despite opposition at home after his election in 2013.

The agreement with powers led by the United States, the Islamic republic's bete noire, has raised hopes of recovery in Iran. But although the economy exited a deep recession in 2014-2015, growth has stagnated in the past year.

The run-up to polling day was overshadowed by the exclusion of thousands of hopefuls by the Guardian Council which vets all candidates for public office for loyalty to the Islamic revolution.

Reformists said they were worst hit.