A total of four animal protection agents for the SPA and two police officers are searching the area for a female dog and her pups.
The dogs are described as being tall, black and white and of a mixed breed. The mother weighs about 45 pounds.
The incidents happened around a walking and bike path between Irwin Street and Saint-Jude Street near the city's industrial park.
Officials say the dogs attacked and bit a woman and her dog on Friday. The woman suffered injuries to her hand, ear and both legs.
The dogs also tried attacking two cyclists on Monday morning but they managed to escape safely.
Karl Girard, spokesman for the Eastern Townships' SPA, said the female dog and her pups surrounded him while he was searching for them in the woods. He got away unscathed.
Girard added it appears the dogs have been gathering food for the winter since dead rabbits and other animals were found in holes in the ground. Girard said the mother may be pregnant and hunger may be behind her aggressive behaviour.
He also said that this is an unusual circumstance but that she must be killed because of her aggressiveness.
A four-month-old pup was killed Monday and a trap was set to try and capture the rest of the pack.