NEW YORK (Reuters) - New York officials expect by Sunday to complete a city-ordered cleaning of cooling towers in the South Bronx that were tied to an outbreak of Legionnaires' disease that has killed 10 people, Mayor Bill de Blasio told reporters on Saturday.

The outbreak appears to have peaked with no new cases diagnosed over the last four days, but the inspection and cleaning of cooling towers will continue as the city battles the Legionella bacteria, which thrive in warm water, de Blasio said.

Some 108 people were sickened in the outbreak, with 18 still hospitalized, de Blasio said.

"This is literally unchartered territory ... We have never seen an outbreak of Legionnaires' like this in the history of New York City," he told reporters. "We also know that this is an emerging reality not just here in this city but around our state and nation."

New York had not previously attempted to list all of the estimated 2,500 cooling towers within its five boroughs. The towers, common on the rooftops of modern buildings, are used for heating, ventilation and air conditioning.

The city turned to a range of technologies from police helicopters to satellite maps available on the Internet to search them out.

Cooling towers in five buildings were identified as the likely origination points for the outbreak, and another 161 buildings in the outbreak area were identified as potentially having cooling towers.

The city is working to have all of the remaining buildings in the area inspected and disinfected within the next 24 hours, de Blasio said.

Citywide, building owners have been ordered to disinfect their cooling towers within 14 days if they have not already done so within the last month. The state is also providing building managers and landlords with free Legionella testing through October.

Officials have stressed that drinking and bathing water are safe to use throughout the city, and using home air conditioning units are also safe.

(Reporting by Daniel Bases; Editing by Scott Malone and Lisa Shumaker)