A major Papa John's franchisee group on Friday publicly urged the chain's founder, John Schnatter, to move on from the company, as it continues to be rocked by the events following his use of the N-word on a conference call.

Schnatter, who owns nearly 30 percent of the company, gave up his post as chairman in July after his use of the term came to light. That followed his resignation from the CEO role in December, after he provoked public outrage by blaming weak pizza sales on "poor leadership" by the NFL amid players kneeling during the national anthem.

The chain's founder has since been locked in a bitter feud with the company, accusing the board of staging a coup and mismanagement. The pizza chain has fallen behind competitors like Domino's in terms of technology and product innovation.

Vaughn Frey, president of the Papa John's Franchise Association, said in a news release provided by Papa John's: "We believe it is time for the founder to move on. (Current Papa John's CEO Steve Ritchie) is pursuing the right initiatives to reinvigorate growth and recognizes the importance of working together to move forward successfully."

Frey's franchise association represents roughly half of the North American franchise system, a Papa John's spokesperson told CNBC.

On Saturday after CNBC's article published, one franchisee within Frey's association contacted CNBC to say he supports Schnatter. The franchisee requested anonymity for fear of retribution.

Also on Saturday, Schnatter contacted CNBC to provided an updated statement. He said, "The franchisees can say they like me or don't like me, or like Steve or don't like Steve, the fact of the matter is we had an eight year run where they made more money than they've ever made... And right now they aren't making any money and they aren't happy."

Frey's statements came as Papa John's announced it is offering a franchisee assistance program in the manner of reduced royalties, fees and pricing on food-service products like dough, to help buffer falls in sales. The company has been facing declining sales since before the uproar surrounding Schnatter, but that trend has accelerated since.

Papa John's earlier this week lowered its outlook for comparable stores growth, saying it now expects them to fall between 7 percent and 10 percent this year, up from a maximum of 3 percent it had previously forecast.

It also said same-store sales between July 2 and July 29 were down about 10.5 percent, which Ritchie blamed on the public outcry surrounding Schnatter's remarks.

Papa John's franchise advisory council, which represents all franchisees, also came out in support of the company and cost-relief program.

Meanwhile, analysts at financial services firm Stephens this week wrote, "While we have been vocal in wanting to see more in the way of innovative value messaging and traffic driving initiatives, we feel strongly that an aggressive focus on the company's new initiatives (particularly brand, value, and technology) present a much greater chance for success vs. remaining tethered to Mr. Schnatter's image."

"We would also note that we believe this opinion is overwhelmingly shared by the investment community," the analysts added.