A 103-year-old woman in Iran has recovered after being infected with the new coronavirus, state media reported, despite overwhelming evidence the elderly are most at risk from the disease.

The unnamed woman had been hospitalised in the central city of Semnan for about a week, IRNA news agency said. But she was "discharged after making a complete recovery", Semnan University of Medical Sciences head Navid Danayi was quoted as saying by IRNA late Tuesday.

The woman was the second elderly patient in Iran to have survived the disease. The other was a 91-year-old man from Kerman, in the southeast of Iran, the news agency said.

After being sick for three days, he recovered on Monday despite having pre-existing medical conditions including high blood pressure and asthma, it added. The report did not say how the pair were treated.

Since Iran announced its first deaths on February 19, the novel coronavirus has spread to all of the country's 31 provinces and killed nearly 1,000 people. The elderly are the most vulnerable to the disease, which first emerged in China late last year.

The World Health Organization this month estimated the novel coronavirus kills 3.4 percent of all those infected. But for people aged over 80 the fatality rate was 21.9 percent, according to a report the WHO carried out with the Chinese authorities.