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The vehicle struck five pedestrians about 1:15 p.m. outside the Church of St. Mark in the 900 block of Coeur d'Alene Avenue, said Ron Myers of the Los Angeles Fire Department.
Police said the driver may have been trying to help her daughter, who had a seizure in the SUV, and her foot accidentally hit the accelerator instead of the brake.
"I turned around and the car came straight for us," Enrique Lopez told a reporter. "And I fell to the ground. Car was inches away from me and then next thing I know, I looked towards the car and my mom's under it. And so she gets up and I help her find my brother and my baby sister."
"I went to the hospital to be with the family," Father Michael Rocha told a reporter. "I was there with her husband. He informed me that they have two daughters, an 11-year-old and a 5-year-old."
The victim and the driver were both parishioners of the church, it was reported.
The other injured pedestrians included a 2-year-old girl, who suffered minor injuries; her 35-year-old mother, who had serious injuries; a 45-year-old woman, who was seriously injured; and a 38-year-old man, who was critically injured.
"There was a guy pinned up -- pinned and dragged underneath the car," Maria Marquez Carnejo told a reporter. "They lifted the car, got the guy that was pinned underneath and laid him there until, you know, help came."
Three women in the SUV, ages 46, 24 and 91, were taken to a hospital with minor injuries, according to the fire department.
"It was just terribly tragic," neighbor Teri Colman told a reporter.