An ambulance stops Thursday Cambridge Rehabilitation and Nursing Center, on Dana Street in Mid-Cambridge. (Photo: Martha Henry)

The three nursing homes in Cambridge each have more than 30 residents infected with Covid-19, the state Department of Public Health reported Monday night. Until then, both the state and the city Department of Public Health had withheld the identity of nursing homes coping with outbreaks.

The more-than-30 cases category was the highest level of infection reported by the state health agency. Of the three homes, only Sancta Maria Nursing Facility on Concord Avenue had previously disclosed that some of its residents had the virus, and that was on a recorded message that did not give numbers. The other two homes are Neville Center, at Fresh Pond, and Cambridge Rehabilitation and Nursing Center, on Dana Street.

Administrators at the three homes couldn’t be reached Monday night. Last week none of them returned calls from Cambridge Day. City Public Health Department spokeswoman Susan Feinberg didn’t respond to an email asking what the department is doing to respond to the outbreaks.

Monday’s report of coronavirus cases from the local health department said 184 residents of nursing homes and assisted living facilities in the city had tested positive for the virus. The city has not disclosed how many live in nursing homes and how many in assisted living. One of the assisted living facilities, Cadbury Commons, previously told The Boston Globe that some residents were infected.

Generally nursing home residents are considered more likely to get the virus than are those in assisted living because they must share space with other residents, and employees go from resident to resident to care for them. Assisted living residents live in their own apartments. Nursing home residents also face high risk if they become infected because of their age and poor health. About half the deaths from the virus in Massachusetts were nursing home residents or workers, according to the state.

Cambridge has not reported the number of deaths among long-term care residents except for six deaths announced April 13. As of Monday, a total of 26 Cambridge residents have died from Covid-19.