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Dr. Lawrence Loh, interim medical officer of health, says the letters were mailed on Tuesday and Wednesday.
He says his team is working quickly to notify these people and make sure they have what they need to manage this difficult situation.
Loh says an investigation found that several positive test slips were mixed with a batch of negative results received from labs.
He says the error was not noticed until after the notification letters were mailed.
Loh says they have made changes to their process to ensure that this does not happen again.
"I know the relief those residents felt for a few moments has sadly been transformed into feelings of fear and uncertainty," he said Thursday in a release.
"On behalf of the Region of Peel, I extend apologies to those residents impacted by this error."
The Region of Peel includes more than 1.5 million people and 175,000 businesses in the cities of Brampton and Mississauga and the Town of Caledon.
This report by The Canadian Press was first published April 2, 2020.