Charest says his government will look into the outbreak to determine what could have been done differently.
Three new cases have brought to 107 the number of people who have contacted the disease in Quebec City since July.
Health officials have set up a toll-free information line at 1-877-644-4545.
The deadly bacteria grow in the stagnant water of cooling systems, spreading in little droplets through air conditioning.
Authorities have disinfected the systems in more than 100 Quebec City buildings but say more cases could surface in the coming days.
Inspectors are going to return to 30 cooling systems over the next few days to look at the water and to make sure building owners have complied with clean-up directives.
Charest, who is in the midst of a hard-fought battle to be re-elected next week, refused to politicize the debate on Monday and said it is not a ''partisan affair.''
''We will assume the share of responsibility that is ours,'' he said during a campaign stop.
''We will look at everything and we will do so rigorously because we're talking about people's health.''
His position clashed with that of his health minister, Yves Bolduc, who has accused the Parti Quebecois of failing to implement recommendations from a report in 1997 when the PQ was in power.
The source of the current outbreak is believed to be the cooling systems of two building towers.
Chantale Giguere, assistant director general for public security in Quebec City, said more than 100 cooling towers have been inspected.
''Beginning tomorrow (Tuesday), we're going to revisit 30 towers that we checked last week,'' Giguere said Monday.
''We want to do turbidity tests on the water — to see how transparent it is — as well as chlorine tests to verify that building owners have complied with what we asked them to do.
''And if we see by Thursday that these tests are not positive, they could be faced with an order to have their cooling towers shut down.''
The Quebec government promised additional steps against the disease following criticism last week from Quebec City's mayor.
The new measures, which may be enacted this fall, include holding building owners legally responsible for maintaining their cooling systems.
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.
The current spate is not considered the largest legionella outbreak in Canadian history.
In 2005, 23 people died and more than 100 others contacted the disease at a home for the elderly in Toronto. The bacteria were traced to a cooling tower at the facility.
A molecular biologist with Public Health Ontario says dealing with the disease is really complex because it is so common.
''It's basically found everywhere in water sources,'' said Cyril Guyard. ''It seems to concentrate in man-made water systems."
''Because it's so ubiquitous, it's found everywhere, it's really complex and challenging to link the environmental sources with the patient cases."
While some hypothesize that hot summers featuring the use of more air conditioning lead to higher rates of the disease, Guyard said he's never seen a study that proves it.
One study has suggested humidity, rather then heat, might be correlated to an increased number of cases.
— With files from Helen Branswell in Toronto and Fannie Olivier