After walking into the produce section of a Publix supermarket filled with lunchtime shoppers in Florida, a shooter fatally shot a woman and her grandson before turning the gun on himself, police said Thursday, June 10.

The Palm Beach County Sheriff's Office said the shooting happened at around 11:30 a.m. ET in a Publix supermarket at 1100 block of Royal Palm Beach Boulevard in Royal Palm Beach, which is around 15 miles west of Palm Beach in Florida.

Publix Shooting Incident in Florida

Based on the officials at the scene, NBC News reported that a gun was found close to the body of the man who they believe had injuries that were self-inflicted.

On late Thursday, the sheriff's office identified the gunman as Timothy J. Wall, 55, of Royal Palm Beach, Florida. But the police have yet to identify the two victims, a woman and a toddler, who would have turned two years old this month.

Palm Beach County Sheriff's Office Spokeswoman Teri Barbera said investigators believe that the woman was shopping with her grandson when the Publix shooting incident happened. 

Barbera noted that authorities are now trying to determine the relationship between the woman and the gunman. She added that it is possible they knew each other.

One of the witnesses, Juan Guardia, said he was near the area when the shooting incident happened. Guardia recalled that a woman Publix worker was shouting to run because there was a shooting incident.

The witness also shared that everything happened fast and everyone was running, and some of the employees were crying.

During a news conference, Barbera said that detectives were interviewing witnesses and reviewing surveillance-camera video as part of the shooting incident's investigation.

As of Thursday night, authorities said there was "no known motive or relationship between the gunman and his victims." 

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Royal Palm Beach's Witnesses and Residents

Meanwhile, onlookers present outside the shopping plaza expressed that they were shocked about the deadly Publix shooting. It is also happened days before the 5th anniversary of the deadly rampage at the Pulse nightclub in Orlando, Florida, which killed 49 people and wounded 53.

One of the regulars at the shopping center, Tracy Greene, said the place is a friendly Publix, and it is crazy that the shooting incident happened there, the USA Today reported.

Even Tracey Cohron, another Royal Palm Beach resident who often shops at the Publix, said she has been in the place for more than 20 years, and she cannot believe what happened. She noted that she knows so many people who work there, and it is scary. And if she left her home earlier, she added that she might be inside the store when the shooting happened.

County Commissioner Melissa McKinlay expressed sympathy for the victims, families, those who witnessed the shootings, and first-responders. She said there is a need for a conversation to prevent another shooting violence.

The sheriff's office sought to calm people's worst fears because of the incident. They posted on social media that detectives are investigating the shooting that took place inside the Publix.

They also noted that deputies located three individuals who died from gunshot wounds upon arrival - one adult male, one adult female, and a toddler.

They have also confirmed that the shooter is one of the deceased. They also said that it was no longer an active shooter situation, Palm Beach Post reported.

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WATCH: Several Unanswered Questions After 3 people Fatally Shot at Publix in Royal Palm Beach - From WPTV News