Kenney, a possible 2015 mayoral candidate, launched an effort this year to end mandatory arrests for people caught with less than an ounce of marijuana.
He said that African Americans were disproportionately targeted in pot arrests and that hauling people to jail for a little pot was a waste of police resources.
"We cannot sit idly by while these kids get arrest records that will follow them forever," Kenney said Monday. "Philadelphia must be a leader on this issue."
The administration balked at his first bill, which would have allowed officers to issue summonses on the street, saying implementation would be a bureaucratic mess.
Kenney's latest bill would downgrade pot possession to the equivalent of talking on a cellphone while driving - an offense that on its own does not lead to an arrest.
But Nutter's director of public safety, Michael Resnick, said in a committee hearing Monday that the new bill still left "operational difficulties" for officers.
His chief complaint was that Kenney's bill would clash with state law. He raised the possibility that other police departments operating in the city could be forced to choose between the city or state versions.
People arrested in Philadelphia, therefore, could face different charges depending on the arresting agency.
"There is no procedural justice in this scenario," Resnick said.
The bill, nonetheless, passed through the law and government committee, with Councilman Dennis O'Brien casting a lone dissenting vote.
"We must have leadership from the administration," Kenney said. "I just think we need to come into the new world."