By 7am, just over 11,400 people had signed the petition.
Duffy said supermarkets were taking more than $1 million in excess profits from shoppers every day.
"These profits are twice what they should be."
Duffy said more competition was needed to drive down prices and give Kiwis a fairer price. But at the moment, that is difficult to do.
"No one is going to start up a competing supermarket without reliable access to wholesale groceries. But the duopoly dominates access to wholesale supply."
He acknowledged the Commerce Commission's recommendation that supermarkets consider supplying other retailers.
"We think this is unrealistic to expect from an entrenched duopoly used to calling the shots. That is why we're launching a petition."
To create what he described as "an even playing field" for new and existing grocery retailers, Duffy said they were calling on Clark to consider regulating access to wholesale supply or setting up a state-owned wholesaler.
Consumer's Sentiment Tracker found people are increasingly worried about the cost of living in New Zealand.
Up to 63 per cent of people in last year's survey picked food and grocery costs as their biggest cost of living concern.
In a recent poll, 98 per cent of those surveyed said they were worried about the price of groceries.