The figure was far higher than Saturday's official data for infections of 271,606 and accounts more than 30 percent of Iran's 80 million population.
"Our estimate is that as of now 25 million Iranians have been infected with this virus and about 14,000 have lost their dear lives", Rouhani said in the speech.
The campaign against the unsafe coronavirus has been underway for the past five months but still, there are concerns inside the country and in the worldwide community about a resurgence of the pandemic, said Iranian President Hassan Rouhani on Saturday.
The country has refrained from imposing full lockdowns.
"There is the possibility that between 30 and 35 million other people will be at risk", he said.
Iran's President Hassan Rouhani has said lockdowns over COVID-19 pandemic may lead to street protests over economic problems, though in Tehran, authorities have chose to impose some restrictions again over newly spiking reported deaths from the coronavirus.
Before Iran reported its first cases of the virus in February, authorities denied it had reached the country for days, allowing the virus time to spread.
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Iran has been battling a resurgence of infections, with official figures showing a rise in both new infections and deaths since a two-month low in May.
The number of Covid-19 infections in the capital city of Tehran has hit an emergency level in the past several days.
The rising toll has prompted authorities to reimpose restrictions in worst-hit provinces after being lifted country-wide in April, with Tehran extending them for an extra week on Friday.
The reported deaths are based exclusively on people who died of COVID-19 in a hospital setting.
Rouhani's deputy head of communications, Alireza Moezi, said on Twitter hours later that the 25 million in fact refers to "those who have encountered the virus and achieved complete immunity".
Even though the president said the estimate is based on a Health Ministry report, it widely diverges from the slightly over 270,000 virus cases officially confirmed so far, leaving the veracity of the estimate unclear.
The Islamic republic has been struggling to contain the Middle East's worst COVID-19 outbreak since announcing its first cases in mid-February.