Author Margaret Atwood, Green Party leader Elizabeth May and actor Gordon Pinsent are among those behind an online petition to rename the public holiday, which is celebrated on Monday, as "Victoria and First Peoples Day."
Peter Keleghan, an actor and spokesman for the group, says the new name would give Canadians a chance to honour both the Crown and the indigenous peoples of Canada.
"I know there is a great deal of monarchists in this country but I think also that there is also an awful lot of talk about how First Nations people, Inuit people, indigenous people in this country are being treated," he said Sunday.
Victoria Day marks the birthday of Queen Victoria and is celebrated every year on the last Monday before May 25. Quebec celebrates National Patriots' Day on the same day, to honour the rebellion against the British in 1837.
There is already a day to honour Canada's indigenous peoples, but Keleghan pointed out it's not recognized as a federal public holiday.
National Aboriginal Day is celebrated every year on June 21.
Keleghan said the group is trying to spread the word about the proposed name change on social media. He's hopeful the message will gain traction in the days to come.
The petition, which is posted on the group's website, victoriaandfirstpeoplesday.ca, calls on Harper to recognize the country's history.
"For centuries, Canadians, the First Nations, the Inuit, and the Metis have had a close affinity with the British Monarchy," the petition says.
"The newly named holiday would be an opportunity to commemorate that venerable relationship, to celebrate unique Indigenous cultures, to revisit our shared history, and to provide an opportunity for all Canadians to participate in the diverse and extraordinary heritage of our country."
Singer-songwriter Susan Aglukark, one-time NDP leadership candidate Brian Topp and Thomas King, an author who often writes on First Nations issues, have also signed the petition.
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