Reformist and moderate Iranian politicians allied with President Hassan Rouhani have won the most seats in the second round of parliamentary elections, state media have reported.

Of the 68 legislative seats being contested on Friday, 33 went to the pro-Rouhani List of Hope coalition and 21 to conservatives, according to the Fars news agency.

That would give reformists 128 seats in the new 290-member parliament, 18 shy of a majority but more than their rivals' 124 MPs. Remaining seats went to independents who could hold the balance of power.

The outcome, if confirmed officially, would represent a dramatic realignment in the country, with conservative MPs likely being outnumbered by their rivals for the first time since 2004.

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It would also be an implicit public vote of confidence for 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.

Preliminary results also took to 17 the number of women elected - eight more than currently and the highest tally since the Islamic revolution in 1979.

Although Iran's parliament has marginal powers - under the country's theocratic rule senior clerics can veto legislation - the result could open a delicate path to limited social and cultural change.

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In stark contrast to the first two-and-a-half years of his presidency the election result should give Rouhani a parliament that supports his government. The outgoing conservative-dominated chamber repeatedly blocked Rouhani and even impeached one of his ministers.

The president's backers made huge gains in the first round on February 26, but reformists still scored eight fewer seats than conservatives overall.

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