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.
In this photo released by the official website of the office of the Iranian Presidency, President Hassan Rouhani adjusts his face mask in a meeting of the national headquarters of the fight against the COVID-19, in Tehran, Iran, Saturday, July 18, 2020.
Despite his estimate as well as urging citizens to take precautions, the country will not reimpose lockdown restrictions.
Iranian President Hassan Rouhani said Saturday an estimated 25 million Iranians have been infected with the new coronavirus, according to state media.
It appears to be the first time a senior official has indicated the country is seeking to defeat COVID-19 via herd immunity.
A man walks past Mofid Children's hospital, where children suspected of being infected with the coronavirus disease (COVID-19) are treated, in Tehran, Iran, July 8, 2020.
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In the last week, the state's seven-day average of positive coronavirus tests rose from 7,876 on July 6 to 8,211 on Monday. Cases have increased 47% over the past two weeks, while hospital admissions have jumped 28% during the same period.
More than 200,000 people have been hospitalised, he said, adding the ministry expected that another 200,000 might need hospital treatment in the coming months.
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. In the coronavirus pandemic, they have been used by countries to survey samples of the population and estimate overall infection rates - whether or not people have had severe, mild or no symptoms of COVID-19.
"A report from the research department of the health ministry has assessed that 25 million Iranians have been infected with the disease so far", Rouhani said, according to the semiofficial Fars news agency.
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".
Iran has been struggling to contain the Middle East's worst virus outbreak since announcing its first cases in mid-February.
All along, Rouhani has tried to keep the economy open and restrictions imposed in the country have been slow to come, short-lived and haphazard.