The company said handlers at San Francisco International Airport in the US took the dog out of his crate on Monday after his flight was delayed and the pet slipped out.
Air Canada said the dog - an Italian greyhound named Larry - bolted, and was last spotted about 8km from the airport. The local CBS TV station said it asked the airline about its procedures after obtaining a statement about the incident.
In response, an e-mail from spokesman Peter Fitzpatrick, urging his colleagues to ignore the inquiry, was accidentally sent to the station, AP reported.
The station said the e-mail read "I think I would just ignore, it is local news doing a story on a lost dog. Their entire government is shut down and about to default and this is how the US media spends its time."
Word quickly spread online, with many voicing their outrage over the company's response.
The airline addressed the controversy in a statement on Friday: "Air Canada acknowledges inappropriate comments were made..." Larry's temporary owner, Ms Jutta Kulic, said: "It was an incredibly stupid, very cold, callous e-mail."
Ms Kulic said she was taking care of Larry after his owner, a friend of hers, died of cancer.
Air Canada said it was searching for Larry and had put up posters near the airport.
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