Six men are being treated in hospital after being confirmed as having Legionnaires' disease.
A further four suspected cases in the south west area of Edinburgh are being investigated, said NHS Lothian.
Five of the men are in intensive care while one is being treated at a high dependency unit. All 10 cases are linked geographically to the Dalry, Gorgie and Saughton areas of the city, said the health board.
NHS Lothian said samples had been taken from four cooling towers in the area while investigations into the source of the outbreak continue.
It said other possible sources are not being ruled out but those responsible for maintenance at these locations have been advised to carry out additional chemical treatment to the water in the cooling systems as a precautionary measure.
Duncan McCormick, consultant in public health medicine and chair of the incident management team, said: "Investigations into the possible source of this outbreak are ongoing and we continue to urge anyone who develops symptoms of Legionnaires' disease to contact NHS 24 or go to their GP."
The health board said Legionella bacteria is commonly found in sources of water, such as rivers and lakes. The bacteria can end up in artificial water supply systems, including air conditioning systems, water services and cooling towers.
Legionnaires' disease is contracted by breathing in small droplets of contaminated water. Symptoms include mild headaches, muscle pain, fever, a persistent cough and sometimes vomiting and diarrhoea.
About half of those with Legionnaires' disease will also experience changes to their mental state, such as confusion. The condition is not contagious and cannot be spread directly from person to person.
The source of the outbreak continues to be investigated by officials from the City of Edinburgh Council's Environmental Health Department and the Health and Safety Executive.