Reformist and moderate Iranian politicians allied with President Hassan Rouhani won a big victory in second round parliamentary elections and capped a remarkable comeback Saturday after years of isolation.

The outcome represents a significant realignment of competing factions in the Islamic republic, with conservative MPs losing their dominance and being outnumbered for the first time since 2004.

It was also an implicit public vote of confidence in Rouhani, who won a landslide election victory in 2013 and went on to clinch a historic deal with world powers over Tehran's nuclear programme that lifted sanctions.

Official results also showed 17 women were elected -- eight more than at present and the highest female representation since the country's revolution in 1979.

Almost a quarter of parliament's seats were at stake in run-offs Friday in what was a showdown between reformists and conservatives seeking to influence the country's future.

Although Iran's parliament has marginal powers -- under the country's theocratic rule clerics can veto legislation -- the result will help the government deliver economic reforms such as a new oil contracts law that could tempt foreign majors.

It could also speed up social change demanded by reformists.

Their return as a major force is a shake up for hardliners in Tehran after an era of diplomatic clashes with the West over a nuclear programme that, before Rouhani, had left Iran under threat of military attack.

Most lawmakers who opposed the landmark agreement struck last year after years of talks with Tehran's long-time foe the United States and other leading nations were rejected by voters.

That verdict should make Rouhani's job easier.

Iran does not have rigid party affiliations, making election outcomes notoriously opaque. Some candidates were backed by both camps and others stood as independents.

But of the 68 seats that were contested Friday, 38 went to the pro-Rouhani List of Hope coalition, 18 to conservatives and 12 to independents, according to final results published by the interior ministry.

That gives reformists 133 seats in the new 290-member parliament, 13 shy of a majority but more than their rivals' 125 MPs. Remaining seats went to independents and minorities who could hold the balance of power.

The second ballot on Friday was needed because no candidate won the minimum 25 percent required in the first round.

- A different parliament -

In stark contrast to the first two-and-a-half years of his presidency, the result should give Rouhani a supportive parliament. The outgoing conservative-led chamber repeatedly blocked him and even impeached one of his ministers.

Iran's reformists have encouraged foreign investment, support moves for greater diplomatic rapprochement and seek social change and fewer political restrictions at home.

Their electoral gains in February came just six weeks after Tehran's implementation of the nuclear deal.

Around 17 million citizens were eligible to vote on Friday and polling took place in 21 provinces, but not in Tehran, as reformists won all of the capital's 30 seats in the first round.

Iran's supreme leader Ayatollah Ali Khamenei had urged a strong turnout, saying the vote was no less important than the initial poll.

Mohammad Reza Aref, a partly US-educated engineer and leader of the reformist pro-Rouhani List of Hope, had set a target of at least another 40 lawmakers.

Although that was narrowly missed, gains for the president's allies will make legislative reforms more likely.

The vote also buys some time for Rouhani to try to turn around a struggling economy amid concern over the nuclear deal. He faces a re-election battle next June and would have been severely wounded had conservatives staged a fightback in the second round vote.

Iranian officials including Khamenei have complained that the United States is not honouring its commitments and is in fact taking steps to dissuade non-American banks from doing business with Tehran.

Although the conservatives went backwards two months ago they did not change tack this time round, keeping up pressure over what they say is a silent agenda among reformists to give up the principles of the revolution.

But appeals for backing from Gholam-Ali Hadad Adel, head of the conservative coalition, who lost his own seat in Tehran because of the reformist surge in February, again went unheeded.