Also infected is the son of a prominent politician who advises Supreme Leader Ayatollah Ali Khamenei. The son, Faridedin Hadad Adel, who is also related to the ayatollah by marriage, tweeted that he had gotten the virus after visiting a school in the holy city of Qom, which is an epicenter of the virus in Iran.

State media reported that an Iranian parliament member had died from respiratory failure after being admitted to a hospital with flulike symptoms, raising questions about whether that was also a coronavirus case. The member, Mohamad Ali Ramezani, was from Gilan Province, which has emerged as a second epicenter of the epidemic within Iran, after Qom.

The outbreak has brought life to a standstill in Iran. Officials have temporarily shut down schools, universities and canceled all public gatherings, according to state media.

Masoumeh Aghapour Alishahi, one of the parliamentarians who has tested positive, released a video message asking Mr. Rouhani to shut down all education centers until the crisis is contained.

The Center of Human Rights in Iran, a research and advocacy group based in the United States, has expressed concerns over reports that prisoners in the country are not being protected from the virus and lack access to medicine, hygiene and sanitary products.

Asadollah Abbasi, a member of Parliament who acts as the body’s spokesman, was quoted in state media as saying that the five positive cases had emerged from testing 100 lawmakers. He said other lawmakers would be tested in their own hometowns or in the capital, Tehran. Iran’s Parliament has 290 representatives.

The country’s death toll rose to 43 from 34 on Friday and the number of infected was up to 593 from 388, according to officials cited in state media. Health experts have said that multiplying each death by 50 is offers a rough estimate of the true number of cases, and experts say the real number of cases is likely much higher than what is being reported.