"The reality is it is only a recommendation - and they can't be prosecuted on a recommendation," Mrs McCullough said.
The death of cyclist John Tangiia, 37, in Parnell last week reinforced the need for change.
"It just made me feel sick to my stomach ... It's just a tragic waste of life and I really don't want another family to go through this."
She was hoping to obtain up to 20,000 signatures and wanted to lead a hikoi to Parliament about April.
"It would take about a week and we would hopefully collect signatures on the road."
Mrs McCullough, 52, said her proposal was for all "vulnerable road users", including pedestrians, runners and horse riders.
"It's split into two parts because when you're in the city it is impossible to give a cyclist 1.5m and to try and do so would antagonise drivers so I've looked at making it 1m. But [on] the open road - where most cycling deaths occur - you've really got to give them a 1.5m space."
Mrs McCullough has been running and cycling less after being "spooked" after her sister's death - and she has seen first-hand questionable behaviour not only by drivers, but cyclists too.
"I have to admit I have been staggered at the amount of riders who do stupid, stupid things. So I do know there is [fault] at both sides ... Cyclists should be policed as well."
The memory of her sister - and the way she died - has been the motivation for the petition.
"I often think of her when I'm driving and I come across a cyclist. I always think about her and get paranoid when I see people on the road."
Queensland has just adopted a law requiring motorists to keep 1m from cyclists in 60km/h or slower zones and more than 1.5m in faster areas.
Labour Transport spokeswoman Darien Fenton said she was happy to support the proposal to select committee stage at least.
Associate Transport Minister Michael Woodhouse said he had "tremendous sympathy" for those who had suffered loss. "I support the idea that motorists should provide cyclists with sufficient space when passing, and in fact the ... Road Code suggests that motorists should give cyclists plenty of room when passing them, ideally allowing at least 1.5m.
"However, enforcing such a rule would be difficult as law enforcement officers would have to judge accurately whether motorists are providing a gap of exactly that distance."
He said the New Zealand Transport Agency was establishing an expert panel next month to consider ways to improve safety for cyclists.
The petition
Calls on Parliament to amend the Land Transport Act 1998 to provide for a new rule requiring motorists to give vulnerable road users a passing distance of at least 1.5m on roads where the speed limit exceeds 60km, and at least 1m where the speed limit is less than 60km. Additional penalty of imprisonment or substantial fine if a breach of rule involves injury or death.
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