The petition has received 189,192 signatures and is due to be debated in Parliament on Monday 26 October.
Campaign group CatsMatter is calling for a change in the law so drivers would have to report collisions involving cats.
The group said 70 animal rescue organisations have also signed an open letter supporting changes to protections for cats on roads.
Under the current rules, drivers are required to report collisions involving certain animals, including dogs, if details are not exchanged at the scene. Cats are not included in those reporting requirements.
CatsMatter said the campaign was inspired by cats called Henry and Snowy.
The group is encouraging supporters to contact their MPs ahead of the parliamentary debate and ask them to attend.
The Government has said it currently has no plans to change the legislation.
CatsMatter said: “Families deserve to know when their cats have been harmed, and cats deserve the same basic recognition already afforded to dogs.”
The petition is scheduled to be debated on Monday 26 October.
