Since the outbreak that gave Legionnaires’ disease its name nearly four decades ago, water-cooling towers have been identified as prime breeding grounds for the deadly disease.

But even as cases have increased across the nation, and experts have called for more safeguards, New York City has done little to address the risks the towers pose as they power air-conditioning systems in many large buildings.

Now, as New York faces the largest outbreak of Legionnaires’ disease in the city’s history, Mayor Bill de Blasio and other officials are trying to marshal a more aggressive approach to the disease and to quell concerns raised by seven Legionnaires’ deaths since July 10, all of them in the South Bronx. At a news conference on Tuesday in the Bronx, the mayor said that the total number of cases had risen to 86 and that more cases were expected to be reported, though the outbreak appeared to be ebbing.