Rouhani, speaking in a televised address on Saturday, referenced a new study by the Iranian Health Ministry that has not been publicly released, and he did not cite specifics on how the estimates in cases were reached.
The current official coronavirus case total stands at more than 14 million, according to a tally by Johns Hopkins University.
The president also said more than 200,000 people have been hospitalized and the report predicts that that number will soon be "twice as many as we have seen in the last 150 days.”
The same Johns Hopkins tally sais 271,606 Iranians have been infected with coronavirus, with 13,979 deaths. The pandemic has also further debilitated the country's severely crippled economy, already struggling from U.S. imposed sanctions.
Faced with a spike of 2,166 cases on Saturday and 188 deaths in 24 hours, authorities in Tehran have closed some public spaces such as coffee shops, zoos, amusement parks, boarding schools, and indoor swimming pools and banned religious and cultural gatherings for one week.
It remains the hardest-hit country in the Middle East.
Iran has faced scrutiny about their reporting of coronavirus cases and deaths, which government officials admit are probably well under the actual count.
After denying the existence of the virus in Iran for days after the likely first infection took hold, Iran held mass demonstrations and a parliamentary election, turning out thousands of people en masse.
Two months after the pandemic ramped up, parliament delivered a report in April that estimated the number of people infected at the time was probably “eight to 10 times” higher than the reported figures and said that health officials lacked adequate testing to determine an official prognosis of the virus.
The reported deaths are based solely on people who died of COVID-19 in a hospital setting. Others who may have died at home have not been recorded and some families have opted not to disclose that their loved ones ever had the virus to avoid any stigmas associated with it.
The Associated Press contributed to this report.