Pezeshkian, 69, won the largest number of votes in a first round on Friday that saw him face off against three figures from the conservative camp, all vying to replace late president Ebrahim Raisi who died in a helicopter crash last month.
He garnered more than 10,400,000 votes, while ultraconservative former nuclear negotiator Saeed Jalili came in second place with more than 9,400,000 votes.
The two will compete against each other in a runoff vote next Friday.
In the lead-up to the elections, Iran's main reformist coalition threw its weight behind Pezeshkian, with former presidents Mohammad Khatami and the moderate Hassan Rouhani declaring support for his bid.
Pezeshkian's push for Iran's presidency comes amid heightened regional tensions over the Gaza war, a dispute with the West over Iran's nuclear programme and domestic discontent over the state of Iran's sanctions-hit economy.
'Out of isolation'
The outspoken heart surgeon had publicly criticised the Raisi government over its handling of the death in custody of Iranian Kurd Mahsa Amini, who had been arrested for allegedly violating the Islamic republic's strict dress code for women.
In a post on Twitter, now known as X, at the time, he called on the authorities to "set up an investigation team" to look into the circumstances behind her death.
In recent campaigning, he has maintained his stance, criticising the enforcement of mandatory hijab laws which require women to cover their head and neck in public since shortly after the 1979 Islamic revolution.
"We oppose any violent and inhumane behaviour towards anyone, notably our sisters and daughters, and we will not allow these actions to happen," he said.
Pezeshkian was born on September 29, 1954, in the city of Mahabad in the northwestern province of West Azerbaijan.
He has represented Tabriz in Iran's parliament since 2008, served as health minister in Khatami's government, and supervised sending medical teams to the war front during the Iran-Iraq conflict between 1980 and 1988.
In 1993, Pezeshkian lost his wife and one of his children in a car accident. He never remarried and raised his remaining three children -- two sons and a daughter -- alone.
Campaigning on behalf of Pezeshkian was Mohammad Javad Zarif, Iran's combative former foreign minister who helped secure the landmark 2015 nuclear deal with world powers, which fell through three years later.
The reformist candidate has called for reviving the accord -- which sought to curb Tehran's nuclear activity in return for sanctions relief -- to get Iran "out of isolation".
"If we manage to lift the sanctions, people will have an easier life while the continuation of sanctions means making people's lives miserable," he said during one of his televised interviews.
If he wins the runoff round, Pezeshkian will be tasked with applying state policy outlined by the supreme leader Ayatollah Ali Khamenei, who wields ultimate authority in the country.
