But the strong margin for former nuclear negotiator Hasan Rowhani was not yet enough to give him an outright victory and avoid a two-person runoff next Friday.
Rowhani had 46.6 per cent of the more than 861,000 votes tallied, said Iran's interior minister, Mostafa Mohammad Najjar, well ahead of Tehran Mayor Mohammad Bagher Qalibaf with about 14.6 per cent. Hardline nuclear negotiator Saeed Jalili was slightly behind in third.
It was unclear when the final count would be known. Iran has more than 50 million eligible voters, and turnout in yesterday's election was believed to be high.
Many reform-minded Iranians who have faced years of crackdowns looked to Rowhani's rising fortunes as a chance to claw back a bit of ground.
While Iran's presidential elections offer a window into the political pecking orders and security grip inside the country - particularly since the chaos from a disputed outcome in 2009 - they lack the drama of truly high stakes as the country's ruling clerics and their military guardians remain the ultimate powers.
Election officials began the ballot count after voters waited on line for hours in wilting heat at some polling stations in downtown Tehran and other cities, while others cast ballots across the vast country from desert outposts to Gulf seaports and nomad pastures. Voting was extended by five hours to meet demand, but also as possible political stagecraft to showcase the participation.
The apparent strong turnout - estimated at 75 per cent by the hardline newspaper Kayhan - suggested liberals and others abandoned a planned boycott as the election was transformed into a showdown across the Islamic Republic's political divide.
The interior minister said Rowhani had more than 401,000 votes from the 861,866 counted so far. Qalibaf trailed with nearly 127,000, and Jalili had more than 119,000. The other three candidates were further back.