Addressing a South Los Angeles church congregation that included the girl's mother and sister, Sharpton said Sunday that some local activists had agreed to suspend protests until the Police Department finished its probe.
"There cannot be a knee-jerk reaction when we will always say the police is right," he said. "There cannot also be a reaction, knee-jerk in the community, saying they're always wrong."
Sharpton spoke a day after the funeral of Suzie Pena, whose father, Jose Pena, 34, also was killed by police when a SWAT team raided his business following a 2½-hour standoff that left one officer wounded.
Activists have staged nightly demonstrations since the July 10 shooting, heckling police and waving signs calling officers involved in the shooting "baby killers."
Sharpton, however, said the incident differed from what he says are previous examples of police misconduct. He said the latest case wasn't similar to the 1991 beating of black motorist Rodney King because it was unclear who was at fault.
"I take a different posture this time," he said. "We must fight for justice and I think, if we have confidence, the mayor will stand and make sure that will happen."