Tehran - Reformist allies of moderate President Hassan Rouhani won all 30 parliamentary seats in the Iranian capital, a major boost Sunday that pushed them into a nationwide lead in crucial elections.

Combined with results coming in from more than half the 290 seats up for grabs nationwide from Friday's polls, the pro-Rouhani List of Hope was outpacing its conservative rivals overall.

A clean sweep in Tehran was followed by steady gains elsewhere, according to preliminary results, in a major fillip for the president, signalling overwhelming public backing for his landmark nuclear deal with world powers last year that ended a 13-year standoff.

The election outcome is vital to Rouhani's chances of introducing domestic reform in the form of legislation capable of delivering even limited social, political and economic changes.

The coalition of moderates and reformists representing the president's hopes was on course to wipe out conservatives in Tehran with 90 percent of ballots counted.

In comments posted on Twitter beside a picture of smiling voters, young and old, he said: "With your skilful voting you've created a new atmosphere. In respect, I stand up before you, great nation, who are the pride of the history of the land of Iran."

The elections are Iran's first since sanctions were lifted last month under the nuclear agreement, which included unprecedented talks with the United States, the Islamic republic's bete noire since a revolution in 1979 overthrew a US-backed monarchy.

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

Elsewhere, where 135 seats out of 260 have been declared so far, 38 went to the main conservative list and 30 to the List of Hope.

A further 36 seats went to independents - of whom 16 are known to lean towards conservatives and 13 are close to reformists, with the others of no clear affiliation.

None of the remaining 31 seats had a clear winner, meaning a second round of voting will be needed, which is not expected until April or May.

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

The early results 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 in which dozens were killed. Reformists said that ballot was rigged and their two defeated candidates, Mir Hossein Mousavi and Mehdi Karroubi, have been under house arrest since 2011.

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

The head of the pro-Rouhani coalition, Mohammad Reza Aref, a former vice president, was in first place in Tehran, with 1,323,643 votes.

Ali Motahari, an outspoken conservative MP who has spoken out against the house arrest of Mousavi and Karroubi, switched sides and joined the slate headed by Aref for this election, and was in second spot with 1,185,398 votes.

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 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, 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.

"No one has the power to resist the will of the majority of the people and whomever people don't want must step aside," Rafsanjani tweeted on Sunday.

Many moderate voters stayed away in the 21012 parliamentary election in protest at Ahmadinejad's re-election. But the List of Hope's Tehran landslide suggested they turned out heavily on Friday.