The results were ammounced by the interior ministry said Saturday.
Moderate candidate Rowhani, a former top nuclear negotiator, has collected nearly 1 460 000 votes of the some 3 024 000 ballots counted by 8am (0330 GMT), the ministry said: more than twice as much as his nearest rival.
On the votes counted so far, Rowhani is followed by Tehran mayor Mohammad Baqer Qalibaf with 16%; top nuclear negotiator Saeed Jalili with 13%; and ex-commander of the Revolutionary Guards Mohsen Rezai with 13%. All three of these candidates hail from conservative camps.
More than 50.5 million Iranians were eligible to vote to find a successor to President Mahmoud Ahmadinejad, and Iranian authorities and media reported massive numbers of people turned out for Friday's election.
Earlier, Interior Minister Mostafa Mohammad Najjar said his electoral staff would not "compromise accuracy for speed," dismissing criticism over the pace of the counting process.
No official estimate of turnout has been provided yet.
Rowhani, 64, led talks with world powers over Iran's nuclear ambitions under the presidency of reformist Mohammad Khatami.
He has vowed to mend Iran's ties with the international community, and move to ease western economic sanctions against Tehran over its nuclear drive.
If no candidate gets an overall majority in the first round, the top two candidates will square off in a second-round run-off scheduled June 21. – Sapa-AFP