TEHRAN—Coronavirus infections among Iran’s senior leaders are raising questions over the extent of an outbreak that has become a flashpoint in the world-wide spread of the virus.

A week after Iranian authorities confirmed the first case of the novel coronavirus in the country, at least 34 people have died among 388 confirmed cases, the health ministry said Friday.

But the number of Iranian officials who have tested positive for the virus has drawn attention to the official statistics, with some researchers suggesting the number of infections is far higher—possibly in the tens of thousands.

“It’s now apparent to the world that there is a significant burden of illness in Iran,” said Isaac Bogoch, infectious-diseases physician at the University of Toronto and co-author of a report on the outbreak in Iran published Monday.

Mr. Bogoch and other researchers at the University of Toronto and Dalla Lana School of Public Health estimated the number of cases in Iran at roughly 23,000. With a model used during the 2009 outbreak of swine flu, the researchers estimated with a confidence interval of 95% that between 11,520 and 41,280 were likely infected in Iran.