More than 10,305 people in Ontario have tested negative.
Three of the new cases are in Toronto.
Elliott, meanwhile, said frontline health-care workers should go into self-isolation, noting many deal with patients like those undergoing treatment for cancer whose immunity system is compromised. "We have asked for the assistance of the coroner's office to do a complete examination and investigation to determine whether this person died because of COVID or with COVID".
Speaking with reporters on Wednesday afternoon, Ontario Premier Doug Ford said that about 2,000 COVID-19 tests are being conducted every day.
Elliott said, "for now", Ontario hospitals have an "adequate supply" of ventilators to help seriously ill patients breathe if they come down with severe viral pneumonia after contracting COVID-19, but that the province has ordered another 300.
Officials say they hope to increase capacity to 5,000 tests a day, which would be five times the current rate. "Please know we are actively working with the vendor to resolve any immediate issues and as of this morning added an additional 300 lines", Health Minister Christine Elliott said in a tweet.
The Grey Bruce Health Unit reminds all residents who are returning from worldwide travel and become ill with respiratory symptoms such as a cough and fever should report their travel history to any health professional, or any emergency room before they visit.
In response to a question about a four-day waiting period to get results of a COVID-19 test, Elliott said there has been a surge in people who want to be tested.
"We know that with many borders shutting down we need to find our own sources internally".
A third case of COVID-19 has been lab-confirmed in Grey Bruce.
Dr. Barbara Yaffe, Associate Chief Medical Officer of Health, confirmed the number of cases being sent to labs is increasing but she could not pinpoint an exact date for when the province will be capable of handling the increase in testing.
"We are looking at changing to criteria".
With files from The Canadian Press.