“We are forced to intensify regulations and supervisions, starting in the capital Tehran," Rouhani said in televised remarks.
He said government-run coronavirus task-force offices around the country would make recommendations on restrictions and whether to impose one-week lockdowns.
Measures could include “restrictions or shutdowns” of schools, universities, seminaries, mosques, cafeterias, sports and cultural venues, hair salons.
“If provincial governors deem it necessary, these centers will have to close for a week,” Rouhani said.
He said the stepped-up restrictions would include punishment for not wearing a face mask or breaching the health protocols in public places.
Iran’s health officials have expressed alarm over a surge in infections, urging the country to respect health protocols to control the spread of the disease.
Iran’s death toll from the coronavirus rose by 172 to 25,394 from Friday to Saturday.
On Friday, Iran announced the highest single-day death toll since it registered 216 deaths on August 1.
Iran’s Health Ministry spokeswoman Sima Sadat Lari said the identified cases rose by 3,204 to 443,086 during the same period.
Of the new cases detected, 1,274 patients have been admitted to the hospital, Lari added.
At least 372,051patients have recovered from the coronavirus infection so far or have been discharged from hospitals across Iran, the spokeswoman said.
Among those undergoing treatment in medical centers at present, 4,041 coronavirus patients have critical health conditions, Lari said.
She also said more than 3,905,352coronavirus diagnostic tests have been carried out in Iran so far.
Since the virus outbreak in the country in February, Iran has been trying to produce a vaccine to treat coronavirus patients.
IRNA and Reuters contributed to this story.