Thursday's announcement came hours before public health officials announced the number of overall cases of the disease in Quebec City had jumped to 151 from 141.
Cooling systems in two building towers are believed to be the source of the current outbreak. Local authorities have disinfected the cooling systems in more than 100 buildings.
Inspectors are currently revisiting about 30 of them to look at the water and to make sure building owners have complied with clean-up directives.
A grieving relative held a news conference on Thursday with her lawyer, with whom she has discussed the possibility of a class-action lawsuit.
Lawyer Jean-Pierre Menard, an expert on class actions in the health field, says legal action is not being considered yet but that he wants to know more about what happened.
Menard was accompanied at the news conference by Solange Allen, whose husband Claude Desjardins died of the illness on Aug. 19.
The woman said her husband was dead less than a week after the first symptoms showed up.
"My husband fell ill and had the shivers and a fever during the night Monday and we thought it was just a regular flu," she said.
"He went to work. But then on Wednesday (Aug. 15) his condition worsened."
Allen said Desjardins went to a local clinic Thursday and was rushed to hospital, where blood samples were taken.
"What I don't understand is that the doctor never talked to us about legionnaires' disease," she said.
Desjardins returned home but then had to be rushed to the emergency room of a local hospital where he died on the Sunday, just before noon.
"It was fast and during all that time, I never heard anyone talk about legionnaires' disease — never, ever," she said.
"My husband was the fourth death and there was really criminal negligence there."
Menard said he has plenty of questions about what went wrong.
"We can't help wondering what happened — was there a failure somewhere in the system?" he told the news conference.
"We are dealing with public health. The public has a right to expect, and expects, a very high degree of attention, competence and action when necessary, from the public authorities who handle these issues."
Public Security Minister Robert Dutil said he consulted Quebec coroners who agreed with him that it was necessary to go further than just holding a coroner's inquest.
"Under the circumstances, we want a public inquiry because there's an obligation to testify and it allows us to get deeper into things to avoid it happening in the future," he said in an interview.
Dutil said he will let public health officials do their work and try to find out the cause of the illness so that the epidemic stops.
"We don't know the cause, but it's not up to me to get involved."
The deadly bacteria grow in the stagnant water of cooling systems, spreading in little droplets through air conditioning.
Heavy smokers and people with weak immune systems are most at risk of catching the disease, which is not contagious.
Symptoms include persistent fever, coughing and difficulty breathing.
It can be treated with antibiotics. There has never been a documented case of drug-resistant legionella.