A woman shot her two young sons Saturday, killing a 5-year-old boy and critically wounding his 1-year-old brother, police said.

The woman called 911 about 8:30 a.m. and told a dispatcher that she had killed her children, Los Angeles police Officer Norma Eisenman said.

When police arrived at the apartment complex in South Los Angeles, the woman, believed to be in her mid-20s, was standing on a second-floor balcony waving a handgun and telling officers to shoot her.

The woman shouted, "I've wasted my life," neighbors told the Los Angeles Times.

Officers ordered her numerous time to drop the gun, but she refused. At one point she climbed onto the balcony rail and stood on it, as if preparing to jump, police said.

When she eventually put the gun down on the balcony floor, officers quickly tackled and arrested her, police said.

Investigators had not confirmed her identity Saturday afternoon, Eisenman said.

The 5-year-old was declared dead at the scene. The younger boy was shot multiple times and was hospitalized in critical condition.