Newsom said he will meet Monday with animal control officials to discuss what steps to take to prevent future attacks. His comments came two days after sixth-grader Nicholas Faibish was viciously attacked in his home by one or both of his family's pit bulls.
"We have to be realistic," Newsom said. "You've got dogs that literally can kill. We've seen it demonstrated. If we can't change people's behavior and make them think what's in their best interest, then that's when government comes along and becomes a bit paternalistic."
He said "having a pit bull ... and three kids is not acceptable because we're not going to deal with the consequences of losing a life." Nicholas Faibish was one of three children.
Police say he was alone in the apartment at the time of the attack and was later found by his mother at about 3 p.m. Friday, covered with blood from multiple wounds.
He said he currently has no specific proposal but a decision on legislative action will likely be made within a week. Mayoral spokesman Peter Ragone said a blanket ban is not being considered. A number of other possible restrictions will be discussed in the next few days, but he said it was too early to discuss details.
Officials are still uncertain if both dogs were involved in the attack. Investigators conducted an examination of the body of the female pit bull, Ella, who was shot and killed by police.
Police say Ella was shot because she wouldn't let police into the house. The male pit bull, Rex, was later found under the house - in the backyard.
Blood was found on Rex's fur, but a spokeswoman for Animal Care and Control declined to disclose any other details. Rex is being held at the animal shelter while the investigation continues.
Animal behavior experts have theorized that the attack could have been linked to different stresses on the dogs, including the family's imminent move to Oregon and the possibility that the female dog was in heat, triggering increased aggression in the male.
"I've seen those kids grow up. They're good kids. It's devastating. It's terrible," said Lew, identified as a friend of the family, in an interview with CBS News Station KPIX-TV, adding that the dogs had never been a problem. "Those animals, I've seen people come right up to them and pet them, people right off the street. This is something out of the norm."
The incident has rattled San Francisco dog owners. Animal Care and Control spokeswoman Deb Campbell said that several people arrived at the shelter on Saturday to drop off their pit bulls.
"The pit bulls that killed the boy were described as friendly, and people start looking at their friendly dog and asking if it could do the same thing," Campbell said.
San Francisco has had at least one other fatal dog mauling in recent years, the death of in January 2001. The 33-year-old college lacrosse coach was killed by two 100-pound-plus Presa Canarios in the hallway outside her Pacific Heights apartment.
That case did lead to criminal charges and convictions, and the jailing of the dogs' two owners.