The daily death toll from COVID-19 peaked at 239 this week in Iran, the worst hit country in the Middle East.
On Saturday, the health ministry reported 195 deaths in the past 24 hours, taking the total toll to 28,293. There were 3,875 new cases, ministry spokeswoman Sima Sadat Lari told state TV.
Masks have been compulsory in indoor public spaces since July.
Rouhani said in televised remarks that anyone caught outdoors without a mask in the capital would henceforth be fined 500,000 rials and those infected with the coronavirus who do not self-quarantine or inform friends and colleagues of their illness would be fined 2 million rials.
Schools, mosques, shops, restaurants and other public institutions in Tehran closed for a week on Oct 3 in an effort to curb the spread of the virus. The city's governor extended the closure on Friday for another week.
The Iranian rial fell to a new low against the dollar on Saturday as the country reels from the pandemic and US sanctions. The dollar was selling for as much as 304,300 rials on the unofficial market, up from 295,949 on Friday, according to foreign exchange site Bonbast.com.
Meanwhile, Mohammad-Baqer Nobakht, a vice president in charge of economic planning, became the latest official to be infected by the coronavirus. "I am under observation. Thank God my general condition is good," he tweeted.
Two other vice presidents had been infected earlier and at least two senior officials have died of COVID-19.
The United States slapped fresh sanctions on Iran's financial sector on Thursday. Tehran has accused Washington of undermining its ability to pay for basic necessities during the pandemic.