The father, said to be in his 30s, was found in his car bleeding from stab wounds to the chest, his dead sons in the back and a knife in the passenger seat yesterday.
The boys, ages 8 to 12, were pronounced dead at the gruesome scene.
The father, whose name was not released, is the only suspect in the killings, police said. He was taken to a hospital in critical condition and will be arrested if he survives his wounds, Los Angeles Police Officer Matthew Ludwig said.
"These are horrific incidents," police Chief Charlie Beck said. "These are incidents that have scarred not only a community but the first responders that have to handle them."
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"It is a sad day in LA," he said.
The three boys did not attend the elementary school next to the crime scene, Beck said, but they are enrolled in the Los Angeles Unified School District.
Beck said the boys' mother is deceased and that their step-mother was safe and being interviewed by detectives.
The deaths come as homicides are on the rise in Los Angeles.
In August, 39 killings drove a year-to-date uptick in murders in the nation's second-largest city, according to police statistics. The 39 killings in August are compared with 22 the previous month and 19 last August.