The outcome, if confirmed officially, would represent a dramatic political realignment in the Islamic republic, with conservative MPs likely being outnumbered by their rivals for the first time since 2004.
It would also be a huge 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.
Voting was extended yesterday in the second round elections for almost a quarter of parliament's seats in what was a crucial showdown between reformists and conservatives seeking to influence the country's future.
It is also likely to herald a parliament that supports the government -- the current conservative-dominated chamber has repeatedly blocked Rouhani's initiatives and even impeached one of his ministers.
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The president's backers made huge gains in the first round of elections, on February 26, when voters drove many conservatives out of the parliament, but still scored eight seats less than them overall.
Of the 68 seats being contested yesterday, 33 went to the pro-Rouhani List of Hope coalition and 21 to conservatives, according to the Fars news agency, an outlet close to conservatives.
Another conservative news agency, Tasnim, said Rouhani's allies had won 35 seats in the second round, which was needed because no candidate won the minimum 25 per cent required in the first ballot.
Tension over the Friday vote's high stakes was underlined by a shooting involving supporters of rival candidates in a southern province. The rare political violence left four people wounded, a security official said.
Their electoral gains in February came just six weeks after Tehran's implementation of a nuclear deal with world powers under the moderate Rouhani.
Around 17 million citizens were eligible to vote yesterday and polling took place in 21 provinces, but not the capital Tehran, as reformists won all of the capital's 30 seats in the first round.