The figures, which Mr Rouhani said were based on a new Health Ministry report, are far higher than Iran’s official toll of 269,440 infected. The President, in a televised speech, did not address the discrepancy.
Iran, with a population of more than 80 million, has been the Middle East country hardest hit by the epidemic.
“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,” Mr Rouhani said in the speech.
“There is the possibility that between 30 and 35 million other people will be at risk,” he said.
“In total, more than 200,000 people have been hospitalised,” he said.
The Health Ministry on Friday said 13,791 people had died from Covid-19.