Coun. Alfred Moses and resident Julie Morrison canvassed Inuvik, questioning whether or not people would like to see restaurants go smoke-free.
Of the 364 names on the petition, only five disagreed.
Morrison said they were pleased with the response.
"We're looking at roughly 10 per cent of Inuvik's population, which is really good," Morrison said.
Across the country, municipalities and provinces have enacted similar legislation and Morrison thinks Inuvik should do the same.
"I think people fully realize the dangers of second-hand smoke," she said.
In Inuvik, smokers can puff away freely in restaurants.
"People want the option of going to places where they can enjoy a meal without having to be around smoke," she said.
"There isn't a place like that here, except for Cafe Gallery."
Mayor Peter Clarkson, and his wife, Sue, opened Cafe Gallery in 1994 as the first non-smoking restaurant in the NWT.
Peter said they felt people would enjoy having a clean-air environment.
"We had it from both sides; people walked out and other people appreciated it," Peter said. "It got to be a gathering place for moms and tots during the early part of the day."
"Overall, I think we had more people coming because they knew it was smoke-free."
The Clarksons no longer own the Cafe Gallery.
In Yellowknife, restaurants have gone smoke-free and so will bars, effective April 1.
"We gave all councillors a draft of a bylaw that would be very similar to Yellowknife's current bylaw," Clarkson said. "Not that we're considering going to that extent, but we just wanted council to look at what all the options were."
He said council plans discussions with residents and business owners before the bylaw will be drafted.
The petition will go to the administrative committee to review and bring suggestions forward to council.