The Guardian Civic League held a press conference Thursday night in North Philadelphia.
Ralston was fired after admitting he made up a story of being shot by two black men last month.
Ralston, a 21-year veteran, told police he was on patrol in the city's Overbrook section early on April 5 when he stopped two black men for questioning along some railroad tracks.
He told investigators that one of the men put a gun to his head, but that he knocked the weapon away and suffered a graze wound to the shoulder when it fired, investigators said. Both men fled, he said.
Police combed the neighborhood for hours looking for the men. Officers never stopped or arrested anyone matching Ralston's description of the gunman, Ramsey said.
Investigators quickly found inconsistencies in his story. Forensic evidence didn't match Ralston's story, investigators couldn't find a shell casing, and gunpowder on Ralston's shirt matched the kind of powder used by the department, Ramsey said.
The Fraternal Order of Police had put out a $10,000 reward for information leading to the alleged suspect.
On Tuesday, FOP President John McNesby condemned the sergeant's actions, saying they took away from the good work of police officers.
"Nobody knows what he was thinking to do something like that," McNesby said. "He wasted a lot of time, a lot of manpower. It could really stir up a lot of stuff in the city when you don't really need it."
In exchange for the truth, Commissioner Charles Ramsey agreed not to press criminal charges.
Leaders say that's not acceptable.
"So if the city made a deal, we want to go outside of them and get the US Attorney, US Justice Department to come in here and file charges against Sgt. Ralston because there is no way he should not be charged criminally," Rochelle Bilal, the president of the Guardian Civic League, said.
The League says Ralston's actions only reinforce racial stereotypes they are trying to overcome.
--------------
The Associated Press contributed to this report.
