"I think the obvious question everyone has is who takes loaded weapons into a Toys "R" Us?" he said. "I doubt it was the casual holiday shopper."
City spokeswoman Sheila Gilligan said police told her the shooting broke out between "two groups of individuals that have a dispute with each other."
The Palm Desert Police Department received calls of shots fired around 11:35 a.m., Riverside County sheriff's Sgt. Dennis Gutierrez said. He said officers were still investigating what prompted the gunshots.
Immediately after the shooting, about 20 people rushed into the World Gym across the street from Toys "R" Us, the gym's assistant manager Glenn Splain told The Associated Press in a telephone interview.
"They were crying, tearing and shaking," Splain said, adding that one woman came in cradling a baby.
"Some people got into a fight," said Splain, who spoke with some of the customers. "One of the guys here thought it was over a toy, but it got louder and louder and then there were gunshots."
Sarah Pacia of Cathedral City told The Desert Sun newspaper she was in the store with her two boys, ages 4 and 6, looking at coloring books when she heard a commotion in the next aisle. She thought it was people rushing to get a sale item. Then she heard three or four shots.
She said she froze, and store employees calmly escorted her out of the store.
"This is Toys "R" Us. There are kids shopping in there," Pacia said. Her son Jayden, 4, was clinging to her leg. He told her he didn't want to die, she said.
Toys "R" Us officials did not immediately return calls seeking comment.
Palm Desert is a resort town about 120 miles east of Los Angeles.