An 80-year-old California man who came home to find two burglars in his house says he shot and killed one of them despite her pleas she was pregnant, but her alleged accomplice has been arrested on suspicion of murder.

Police said they would present their case to prosecutors on Friday but were uncertain whether to recommend charges against Tom Greer, who told a television station he shot the fleeing woman in the back.

"She says, 'Don't shoot me, I'm pregnant – I'm going to have a baby,' and I shot her anyway," Greer told KNBC-TV outside his house. "The lady didn't run as fast as the man, so I shot her in the back twice," Greer told the TV station.

Long Beach police chief Jim McDonnell said at a news conference on Thursday that 28-year-old Andrea Miller did not appear to be pregnant, but an autopsy would determine whether she was.

The surviving suspect, Gus Adams, 26, was arrested on suspicion of residential burglary and murder. The murder charge is possible because he is accused of being involved in a felony that led to a death, the chief said.

Both Miller and Adams, who had histories of similar crimes, were unarmed, McDonnell said.

Greer had been burgled three times before and believed the same suspects were responsible.

He said both suspects punched him and slammed him to the floor, breaking his collar bone, McDonnell said.

Greer managed to get to another room where he grabbed a gun and opened fire. He chased the suspects outside, where he shot Miller.

McDonnell would not say whether Miller was shot in the back as Greer claimed.

Under Californian law homeowners can defend themselves if they are in imminent danger of serious bodily injury or death. Prosecutors will have to determine whether chasing after the suspects and firing on them outside the home goes beyond self-defence.