Paul Lespérance at a news conference Thursday expressed his "profound sadness" and said the events were unsettling for the staff, the patients and their families.
The hospital announced Wednesday that one of its psychiatric patients had been arrested after an attack on a 71-year-old female patient..
Authorities confirmed they were also investigating a link between arrested patient and the deaths of two male patients, ages 69 and 77, who died earlier this month.
Lespérance said there were no shortages in staff or in security during the attacks.
He said instances of violence are not rare at the hospital and that patients can sometimes act up or get verbally abusive.
Lespérance said that the man who died on June 16 had suffered from serious health issues, and no immediate suspicions were raised.
Hospital staff contacted police after the attack on June 22, and authorities then turned their attention to the two recent deaths.
Notre-Dame Hospital cares for patients of varying ages and care levels.
Suspect admitted on date of 1st death
Montreal police arrested Idelson Guerrier, 31, also a patient at the hospital, while investigating the attempted suffocation of a patient in the psychiatric ward Friday.
Guerrier was arrested and charged with attempted murder. He has not been charged in connection with the killings.
The accused is now undergoing a 30-day, court-ordered psychological evaluation and will make another court appearance next month.
According to Yvan Gendron, the hospital's associate director, Guerrier was admitted to Notre-Dame on June 16, the date of the first death, and placed in intensive psychiatric care and carefully evaluated before being released to the general care unit.
Guerrier's wife told reporters she had asked for her husband to be hospitalized after he started acting "out of character."
Hospital staff did not have access to Guerrier's criminal record or personal information.
Lespérance said that the intensive care unit at Notre-Dame Hospital holds six beds and that two employees are assigned to each patient. The patients are visited every 15 minutes.
Authorities are not releasing information about which floors the suspect or the victims were located on at the time of the two killings or during the attack.
Police investigating link between deaths and attack
Police said the "modus operandi" in the two homicides and the attempted suffocation appear to be the same, but they have to wait for the results of DNA testing before making a definitive link.
"As we were there, authorities from the hospital came forward to police and said they had two suspicious deaths where both patients might have passed away from suffocation," said Const. Yannick Ouimet.
Police released information about those incidents yesterday. They said they are looking for connections between the suspect and the two other deaths, which happened in separate incidents on June 16 and 21.
"We are waiting on results from analysis that was done to try and link this suspect to the two other cases," Ouimet said.
The hospital is conducting its own investigation into the deaths and the attack on the patient.
Notre-Dame contacted all of the families of people still hospitalized in the facility to advise them of the incidents, Yvan Gendron, the hospital's associate director, said Thursday.
He said psychological support is also being offered to hospital staff and patients.
"We're extremely saddened by these events that have touched vulnerable people and their families," he said.
He added that the hospital has rigorous measures in place to ensure patient safety, but they will be reviewed to determine if improvements can be made.
The hospital released information on the arrest and the double homicides 11 days after the first death.
Hospital executives said they did not try to cover up the incidents, but that the case had to be investigated by police. It was only when authorities determined the two deaths were homicides that information was released.
Perceptions of mental illnesses
Lespérance said he believes the events are affecting the public's perception of mental health issues.
"These events project a negative image of psychiatry in a hospital setting. We have fought the stigmatization faced by our patients. We worked hard to promote the importance of social investment. These events come at a time when we thought we had managed to help people understand."