And in a city reeling from the overt danger posed by the virus, top health officials said they had identified another grim reality: The outbreak is likely to have also led indirectly to a spike in deaths of New Yorkers who may never have been infected.

Three thousand more people died in New York City between March 11 and April 13 than would have been expected during the same time period in an ordinary year, Dr. Oxiris Barbot, the commissioner of the city Health Department, said in an interview. While these so-called excess deaths were not explicitly linked to the virus, they might not have happened had the outbreak not occurred, in part because it overwhelmed the normal health care system.

“This is yet another part of the impact of Covid,” she said, adding that more study was needed. Similar analysis is commonly done after heat waves and was performed in the wake of Hurricane Maria in Puerto Rico.

“What New Yorkers are interested in, and what the country is interested in, is that we have an accurate and complete count,” Dr. Barbot added. “It’s part of the healing process that we’re going to have to go through.”

The revised death toll renewed focus on shortcomings in testing that have hamstrung city and state officials since the beginning of the outbreak. A limited number of tests have been available, and until now, only deaths where a person had tested positive were officially counted among those killed by the virus in New York.