It did not immediately identify any of the three people. PBSO said the three dead were a man, a woman and a child. He said the shooter was one of the fatalities.
County Commissioner Melissa McKinlay, who represents the area, said she was told the child was a small child.
At a news conference, PBSO spokeswoman Teri Barbera said the three people were found dead shortly after 11:30 a.m. near the produce section of the store on Okeechobee and Royal Palm Beach boulevards.
Detectives spoke to witnesses and watched surveillance videos as they tried to figure out what led to the shooting.
Authorities have not described the relationship of the three deceased, although Barbera said it was possible they knew each other.
Several patrol cars arrived at The Crossroads shopping center. A PBSO helicopter hovered in the air above the store.
Publix shooting in Florida:What we know about shootings in the Royal Palm Beach shopping plaza
A Palm Beach County fire engine was also on the scene.
Reactions to Publix shooting in Royal Palm Beach
Spectators gathered outside were shocked by the deadly events unfolding.
“This is a friendly Publix. I can’t believe this crazy thing happened,” said Tracy Greene, a regular at the mall.
“I’ve been here for 20 years and I can’t believe this is happening,” agrees Tracey Cohron, a Royal Palm Beach resident who often shops at the Publix. “This is insane. I can’t believe this is actually happening near me.”
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“This is not a Publix problem. This is a people problem,” said Oahtee Moody, a Royal Palm Beach resident who lives across the street from downtown. “I was born and raised here, and I never expected this to happen.”
Publix officials at the chain’s Lakeland headquarters said they were aware of the shooting but referred questions to the sheriff’s office.
“Our thoughts are with those affected by this tragedy,” a Publix spokesperson said in a statement. “We are working with the local police.”
In a statement, McKinlay also expressed condolences to the victims, their families, those who witnessed the shooting and first responders.
But, she said, grieving is not enough. “Tomorrow we need to get up and have a very honest conversation about why this happened and what we can do specifically to prevent this violence. Doing nothing is not an option.”
While a handful of Publix employees were allowed to leave the store, most of the employees and a few customers were kept inside to be interviewed by agents.
Law enforcement officers checked the license plates of cars in the parking lot. People were not allowed to move their vehicles.
PBSO: Shooting took place at Publix in Royal Palm Beach
PBSO tweeted shortly after the incident: “Detectives are investigating a shooting that took place INSIDE Publix in RPB. Upon arrival, officers found three individuals who had died from gunshot wounds, an adult man, an adult woman and a child. The gunman is one of the deceased This was NOT an active shooting situation.”
Check back for updates on this groundbreaking story.