"The incident at Popeyes occurred over 30 years ago. Suggestions that Dr. Carson is lying are outrageous. We will not entertain any further discussion on this issue," Carson's Deputy Communications Director Ying Ma told CNN in an email.
Earlier Friday, Carson said on Sirius XM POTUS Channel that he did not file a police report but believes a Popeyes' employee did.
"I can tell you categorically as a God-fearing Christian, it's something that happened. It's not something I made up," Carson said.
Carson recounted Wednesday a story about being held at gunpoint while a medical resident in Baltimore decades ago.
"I have had a gun held on me when I was in a Popeyes organization," the retired neurosurgeon told Karen Hunter on Sirius XM Radio, referring to the fried chicken fast-food chain.
"Guy comes in, put the gun in my ribs. And I just said, 'I believe that you want the guy behind the counter,'" Carson.
Carson told Wolf Blitzer Thursday that growing up in inner-city Detroit gave him "the sophistication" to know that the gunman wasn't going to murder him but was just looking to rob the place.
Before saying that they would not discuss the incident any longer, the Carson campaign on Friday released a few additional details about the stick up.
Armstrong Williams, the campaign's business manager, said it occurred at the Popeyes on the corner of Broadway and Orleans Street in Baltimore between 1980 and 1983 when Carson was a resident at nearby Johns Hopkins hospital.
Williams said Dr. Carson had gone to the restaurant to get French fries.
Williams told CNN on Friday that Carson recalled people in the neighborhood chasing the robber down the street.
Baltimore police Tweeted on Thursday that Carson's description of the incident provided insufficient information to locate a police report.
Lt. Jarron Jackson, a police spokesman, said Friday that the department would launch a new inquiry using the details provided by Williams. The request was made by CNN.
A spokesperson for Popeyes was not immediately aware of any records of such an incident during that time period.