Hawthorne police spokesman Lt. Scott Swain told the Daily Breeze the decision is for the officers' safety after the uniformed officer shot the dog four times on Sunday.
A cellphone video that had more than 3.9 million views on YouTube by Thursday afternoon shows the dog, named Max, being shot after scrambling out of a car's back seat through a window and lunging at officers who had handcuffed its master.
Witnesses can be heard crying out in distress after watching the dog's grisly death.
The dog's owner, Leon Rosby, said police needlessly killed his dog. His lawyer, Michael Gulden, said Rosby's complaint will be added to an existing lawsuit Rosby has against police.
"I understand that people have been affected by this video. Anyone would be," Swain told the Breeze. "The police officers involved are affected by this incident and having to kill a dog.
"I don't understand how it translates into an eye for an eye: 'We are going to kill you and your family because of this incident,'" he said of the threats to the officers.
Chief Robert Fager has called for calm and urged people to be patient as police investigate the shooting, and also avoid information being circulated through social media because "fallacies are being perpetuated."
Officers in the field have been told to be vigilant against any possible retaliation.
"You'd like to believe that maybe some of the people are just venting, but then you've got to be realistic. There are crazy people out there," Swain said.
Warning: The video is extremely graphic, contains profanity and may be disturbing to some viewers. View it here >>