Rouhani said in televised remarks at the National Headquarters for Managing and Fighting the Coronavirus that the restrictive measures will take effect on Wednesday in 71 cities including 25 of Iran’s 31 provincial capitals for 10 days.
He said the fresh restrictions ban all public gatherings and educational activities.
Stressing the need for strict implementation of the new restrictions, the president said those violating the ban on gatherings, including weddings and memorial ceremonies, must be dealt decisively.
Rouhani added that an operation headquarters will be set up to ensure compliance with the health protocols.
Deputy Health Minister Alireza Raeisi said in a televised press briefing that the new restrictions from next week will include the closure of institutions such as schools, universities, libraries and mosques.
Police meanwhile said on Saturday weddings, wakes and conferences will be banned in the Iranian capital Tehran until further notice.
Tehran police had extended by one week the closure of businesses including beauty salons, teahouses, cinemas, libraries and fitness clubs, according to IRNA.
Police will make unannounced visits to other high-risk businesses, and those that violate health protocols will be shut down, police official Nader Moradi told IRNA.
Total COVID-19 deaths rose by 386 over the past 24 hours to reach 34,864, Health Ministry spokeswoman Sima Sadat Lari said on Saturday, adding total cases rose by 7,820 to 612,772.
She said that at least 481,930 patients have recovered so far or have been discharged from hospitals across Iran.
Among those undergoing treatment in medical centers, 5,185 coronavirus patients are critical conditions because of more severe infection, Lari pointed out.
On Friday, she said that all provinces are still classified as red and yellow or are in alarming situation.
Red is the highest category on the country's coronavirus risk scale.
Iran has opted for a color-coded system of white for low-risk parts of the country, yellow for medium-risk and red for high-risk areas.
Lari said that no scientific research has proven that effective treatment of COVID-19 patients has been found so far. So, the only way to control this global challenge is to follow health protocols.
Following the increase in the number of fatalities and new infected cases in the country in recent weeks, authorities have announced new restrictions across the country to contain the spread of the virus.
Nonessential businesses have been shut in Tehran and dozens of other cities. Schools, theaters and museums have been shut and social, cultural and religious events canceled.
Iranian authorities have blamed the sharp increase on people failing to follow restrictions.
The timing of the pandemic has proved disastrous for Iran's economy, which is under US sanctions reimposed in 2018 after the Trump administration withdrew from the nuclear deal between Iran and world powers.
Reuters, IRNA and Tasnim contributed to this story.