The man killed Sunday night after an hours-long standoff was identified as Jose Raul Lemos, and the girl, about 17 months old, was his daughter, police said. The SWAT officer, who was not identified, was shot in the shoulder and was expected to recover.
"He was using the baby as a shield," Assistant Police Chief Jim McDonnell said.
The man had a 9 mm handgun and a shotgun and was intoxicated on drugs and alcohol, police said. KCBS-TV reporter Greg Mills say police believe Lemos was distraught over a family matter, possibly a custody battle.
"We showed a tremendous amount of restraint, but unfortunately the suspect's actions dictated this," McDonnell said. "It's a true tragedy."
The child's mother, Lorena Lopez, said she pleaded with officers to hold their fire.
"He had problems with depression, his business was not doing well," Lopez told a local television station. "I told them that he needed help, he needs a psychologist, but please don't shoot. They didn't understand, and the police fired, like, 300 shots."
"The officers are taking it very hard," he said. "Anytime you have a baby killed, it takes its toll."
The standoff began at around 3:50 p.m. when officers responded to an area in South Los Angeles west of Watts after residents reported an armed man standing near an intersection with a toddler and behaving erratically and aggressively.
There were three exchanges of gunfire between police and Lemos, who was about 35, McDonnell told reporters. In the final exchange, at around 6:20 p.m., Lemos held the girl as he shot.
"We did everything we could to hold our fire," McDonnell said.
At one point, Lemos retreated into an apartment building, where police said he held the girl hostage.
Police called in a SWAT team and tried to speak with the man; when they at one point attempted to help a neighbor escape the area, he fired at them and they fired back, McDonnell said.
Under police regulations, officers may only fire "when it reasonably appears necessary" to protect themselves or others from death or serious injury.