"Between 30 and 35 million people in the coming months may be exposed to the disease", Rouhani said to members of Iran's coronavirus task force.
Iranian health officials have tried to play down President Hassan Rohani's estimate that as many as 25 million Iranians could have been infected with the coronavirus since the beginning of the outbreak.
The official number of confirmed cases stands at around 270,000, although some official sources and many social influencers have been saying that the government is under-reporting infection and death numbers.
Officially, the virus has so far killed close to 14 000 people and infected more than 269,400 in the country with a population of more than 80 million.
It appears to be the first time a senior Iranian official has indicated the country is seeking to defeat COVID-19 via herd immunity.
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.
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Any cruises touching on a Canada port (such as Alaska & Canada/New England) have been suspended through October 2020. The country is by far the worst-affected worldwide, with 3,576,221 confirmed infections and 138,358 fatalities.
The same Johns Hopkins tally sais 271,606 Iranians have been infected with coronavirus, with 13,979 deaths.
Referring to the Health Ministry report, Rouhani said it also predicts that the number of hospitalizations will soon be "twice as many as we have seen in the last 150 days".
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.
Iran has been battling a resurgence of COVID-19, with figures showing a rise in both new infections and deaths since a two-month low in May.
The Islamic Republic was, and still is, the hardest-hit nation in the Middle East. Saudi Arabia and Qatar - who reported 245,851 and 105,898 cases respectively - are trailing behind Iran in a regional rating.
The rising toll has prompted authorities to make masks mandatory in enclosed public spaces and allow worst-hit provinces to reimpose restrictions, with the capital Tehran among the latest closing some public spaces like coffee shops, zoos, and indoor swimming pools.