WASHINGTON — As the number of coronavirus cases in nursing homes continues to skyrocket, the Centers for Disease Control and Prevention is considering whether to start keeping a formal tally of nursing homes with ongoing cases, according to an agency spokesperson.

The internal decision-making comes amid criticism from Democratic senators who want the agency not only to keep tabs on the number of long-term care facilities with cases but also to name them.

The CDC has never kept a formal tally during the pandemic, but it has computed totals at least twice. On March 23, Seema Verma, administrator of the Centers for Medicare & Medicaid Services, or CMS, said 146 long-term care facilities across the country had at least one case of the coronavirus. Both the CMS and the CDC are part of the Department of Health and Human Services, and Verma was using numbers provided by the CDC.

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A week later, on March 30, the CDC told NBC News that more than 400 facilities were battling the illness, an increase of 172 percent.

Kristen Nordlund, a spokeswoman for the agency, said Sunday that the CDC had no updated figures and that to get the previous tallies of long-term care facilities with cases, the agency had to query individual state agencies.

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The CDC did not say how many states had provided data for its previous tallies. On March 30, the same day the CDC said it had counted more than 400 facilities with coronavirus cases nationwide, NBC News counted nearly 300 in just three states and one county.

In a statement Monday, Nordlund confirmed that the CDC "is not keeping a 'master list' of coronavirus cases in long term care facilities or keeping track of how many facilities have infected residents."

"The number referenced in the CMS press release [of March 23] and updated a week later [on March 30] reflected a snapshot from state health departments responding to informal outreach about their sense of how many nursing homes they were aware of with at least one COVID-19 positive resident," she said.

David C. Grabowski, a professor of health care policy at Harvard Medical School, said he believes the CDC is "completely reliant on state departments of health right now to report this information."

"Some health departments are able to track and report this accurately, while others are not," he said.

Grabowski said the CDC needs to make identifying and reporting the facilities a priority to answer some key questions: "How do we identify and contain COVID-19 in nursing homes if we can't even measure it accurately? How do we learn and implement best practices if we aren't studying the existing cases?"

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Toby Edelman, senior policy attorney for the Center for Medicare Advocacy, said: "If we don't know where the virus is, how can government focus resources where the need is greatest? The public (and residents, families, and staff in particular) need accurate, comprehensive, and timely information. I see no justification in the CDC's putting its head in the sand."

Cases continue to climb rapidly in nursing homes nationwide. In Maryland alone, 81 facilities have cases. And within facilities, the virus is spreading fast. At a state-run facility outside Dallas, there are 89 cases.

In a letter to the CMS and the CDC last week demanding a list of facilities with infections, Democratic Sens. Ron Wyden of Oregon and Bob Casey of Pennsylvania wrote, "At a time when this information could be vital to the health and safety of Americans, it is imperative that the list of facilities with a COVID-19 case, among residents and staff, be made public and shared with relevant health care providers, authorities and Congress on a real-time basis."