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 per cent 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.
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.
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 1,323,643 votes.
The outspoken Ali Motahari, a conservative MP who switched sides and joined the slate headed by Aref, was in second spot with 1,185,398 votes.
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.
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