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SOUTH BRONX — The death toll in a historic outbreak of Legionnaires’ disease in the South Bronx has grown to 12 and two more cooling towers have tested positive for bacteria that causes the severe form of pneumonia, Mayor Bill de Blasio said Monday.

The total number of Legionnaires’ cases connected to the cluster is now 113, de Blasio said, adding that though the totals continue to grow, the number of new cases “continues to taper off.” These newly counted patients were diagnosed recently but became sick before Aug. 3, the last day a new case was confirmed, the mayor said.

There is no evidence of newly contracted Legionnaires’ cases, de Blasio said. Most of the cases have been reported from the South Bronx neighborhoods of High Bridge-Morrisania and Hunts Points-Mott Haven, the city said.

“We have encouraging news that this outbreak has slowed,” city health commissioner Dr. Mary Bassett said.

Among that “encouraging news” are that no one has become sick with Legionnaires’ in the past six days and all cooling towers in the outbreak area have been mapped and cleaned.

Of the 39 cooling towers in the South Bronx that could house bacteria that causes Legionnaires’ disease, 12 have tested positive for Legionnella, the mayor said. All of those towers — which are used to cool down major air conditioning units and are not the same as the iconic wooden water tanks on top of city buildings — have been disinfected or will be disinfected by the end of Monday, he said.

The number of new daily cases peaked July 30 and has been declining ever since, de Blasio said Aug. 4. The mayor added if no new cases appear in the next 10 days — the incubation period of Legionnaires’ disease — that would be an indication they’ve pinpointed and eliminated the cause of the outbreak.

Legislation to prevent future outbreaks such as this will be introduced Tuesday before City Council, de Blasio said. That legislation would require all building owners to register their cooling towers with the city and all new cooling towers to be registered before they can begin operating.

Also included in the proposed law are quarterly inspections, cleaning and disinfection of city cooling towers, and annual certification of those towers, de Blasio said.

Any building owners who do not comply will be penalized, the mayor said, stopping short of revealing the specifics of those penalties.

Health officials insist the city’s drinking water is safe and the cooling towers that tested positive for Legionnella are not connected to the same water New Yorkers use to cook, bathe or drink. Home air conditioning units are also unaffected.

Legionnaires’ disease is a severe form of a pneumonia contracted when a person inhales mist that contains the bacteria Legionnella, according to health officials. Symptoms show up 3 to 10 days after significant exposure and are similar to those of the flu, such as fever, cough and shortness of breath.

The illness was first identified in 1976 at an American Legion convention in Philadelphia when several hundred patients became sick. That outbreak was associated with the convention center’s air conditioning system.