"If he's watching this, the message ... is: Enough is enough. It's time to turn yourself in. It's time to stop the bloodshed. It's time to let this event and let this incident be over," said Los Angeles Police Department spokesman Andy Smith, told reporters at a press conference.
Dorner is accused of killing Riverside police officer Michael Crain, who was gunned down in an ambush last Thursday.
Dorner is also suspected of killing Monica Quan and her fiance, who were found shot to death Feb. 3. Quan was the daughter of former LAPD Capt. Randal Quan, who was mentioned as a target of Dorner's fury in his so-called "manifesto," which he posted on his Facebook page.
In the 6,000 word "manifesto," Dorner outlined his anger at the Los Angeles Police Department for firing him, and made threats against individuals he believed were responsible for ending his career with the police force five years ago.
Dorner's grievance with police goes back five years, to when he was fired after filing what the LAPD determined to be a false report accusing other cops of brutality.
The LAPD assigned 50 protection details to guard officers and their families who were deemed possible targets.