NEW YORK — State health teams will deploy to the Bronx to help collect and test samples from cooling towers amid a deadly outbreak of Legionnaires’ disease as the number of those sickened grew by one to 101, officials said Friday.

Teams will begin work Saturday, and state officials have said they’ll pay for the testing. New York City Mayor Bill de Blasio earlier this week ordered that within the next 14 days, all buildings with cooling towers that haven’t been tested in the last 30 days be tested and any towers found contaminated be disinfected. Failure to comply is a misdemeanor. The bacteria were found in five buildings within a few blocks of one another in the South Bronx, but there is no indication that Legionella has contaminated water systems in buildings.

“A situation like this requires a great deal of detective work. Clearly this is a sleuth mission to find out where this is happening,” said State Health Commissioner Dr. Howard Zucker.

So far, 10 people have died since the outbreak surfaced last month, making it the deadliest in city history, health officials said. The victims were adults with underlying medical conditions. The disease is a form of pneumonia caused by breathing in mist contaminated with the Legionella bacteria.

City Health Commissioner Mary Bassett said officials have a good handle on the outbreak, and the frequency of diagnoses is decreasing.

“We have fewer new cases. People are seeking care promptly and getting treatment promptly. We’re optimistic that we’ve seen the worst of this outbreak, and that our remediation efforts are having an impact,” she said in a statement.

Gov. Andrew Cuomo had asked representatives from the U.S. Centers for Disease Control and Prevention to come help, and he ordered a long-term review on how the outbreak is being handled.

Dr. Claressa Lucas of the CDC defended the city’s response.

“The timing of it (the response) has been very typical,” she said. “I think that they have done a very good job to mobilize their resources. I think they are taking this very seriously, and I am encourages by this response.”

In a television interview Friday, Cuomo touted the state’s response to prevent future outbreaks, declaring, “We can’t go through this again.”

When asked to weigh in on de Blasio’s response to the outbreak, Cuomo demurred, saying only that the “situation became critical” and warranted state assistance.

On Friday, a homeless man who contracted Legionnaires’ disease in the Bronx filed notice with the city that he intended to file a $10 million lawsuit. Marvin Montgomery, 36, remains hospitalized and says he contracted the disease last month while passing out fliers in front of a hospital.

His attorney, Adam Slater, said he believes the city was negligent by “failing to adequately test and monitor to look for Legionella.”

“What you see going on right now is very reactive, which is great and hopefully prevents future outbreaks, but it shouldn’t let their past negligence off the hook for the injured people, like my client,” Slater said. “He has constant headaches, dizziness, he can barely walk and his muscles have deteriorated so much that he can’t even pick up a fork by himself.”

A spokesman for New York City Comptroller Scott Stringer said his office closely reviews all claims.

On average, there are about 540 cases of Legionnaires’ disease a year in New York state. The CDC estimates that 8,000 to 18,000 people are hospitalized annually with the disease in the U.S. Officials at a Cleveland hospital said Friday that a 53-year-old Ohio woman had died from the disease a day earlier.

This story has been corrected to show that an average of 8,000 to 18,000 people are hospitalized in the U.S. every year with Legionnaires’ disease, not that there are about 18,000 cases nationally every year.