Fisherova says she was stunned to hear of the compensation offered to quake families.
Many now-solo parents are having to work weekends and nights to try and make ends meet, she says.
She claimed it was a national tragedy that quake victims are not being more looked after by the Government – especially post-quake inquiries criticised aspects of the search and rescue efforts, and found serious flaws in the design of the six-storey CTV Building.
"New Zealanders should be more aware of how life after the tragedy has unfolded for the families of those who died," Fisherova said.
"In order to survive financially, safeguard their health and their children's futures, the victims' families deserve further compensation. Some of them need it urgently."
The petition was posted on the New Zealand Parliament website on Monday. It closes on March 1.
ACC says it administers the Accident Compensation scheme but has no say in its scope, which is left up to Parliament.
"Our role is to provide the rehabilitation and compensation set out in our legislation to people who suffer personal injury, or to the family members of people who die as the result of injury. We therefore have no discretion to change the amounts payable, even in circumstances such as the Christchurch earthquake," a spokesman said.
Compensation paid by ACC includes weekly compensation, lump sum or independence allowance payments to people who are injured, and funeral grants, survivors' grants, and weekly compensation for spouses and other dependents in the event of death.
"Any review of the legislation to change the amounts payable would be something for MBIE to look at, as they are responsible for the legislation," the ACC spokesman added.
"Of course any payments other than those paid by ACC would be a question for the Government."
By August 2014, ACC had accepted 10,379 claims relating to the February 22, 2011 earthquake, and paid out $53,426,000 in rehabilitation and compensation.
A lengthy and complex police probe into the CTV Building collapse concluded in 2017 that no criminal charges would be laid despite "significant" design deficiencies.