Councillor Chris Wilson said they should request a coroner's inquest into her death.
"It's not about pointing fingers but it's about finding answers for why this happened," he said.
Mayor John Matthews said the accident has had a huge affect on everyone in the community.
"It's been a horrible week for everyone involved," said Mayor John Matthews. "This has been very traumatic."
At the Iqaluit council meeting last Tuesday, councillors said more has to be done to make sure this doesn't happen again.
"In the past three years we've had three accidents," said Coun. Glenn Williams. "Council is going to have to address this and address it quickly." "I want to send my sympathies to Margaret's family and the family of the driver," added Coun. Keith Irving.
Since 2000, there have been three fatal accidents involving Iqaluit city equipment.
Council agreed that there needs to be an external review of the public works department to examine employee safety protocols and the vehicles and equipment they use.
Some of the ideas that council brought forward to improve the department are better training for staff, spot inspections of city vehicles and the creation of a public safety forum.
Currently the onus on inspections is up to the vehicle operator. "The public needs to know that things are being done for their safety," said Irving. The city and RCMP are currently investigating the incident. No charges have been laid.