The ordinance closes a loophole that limits rewards.
Currently, the council is prohibited from putting up rewards when officers are attacked outside city limits.
A majority of Los Angeles Police Dept. officers live outside the city.
The new measure allows for rewards when officers are off-duty wherever the attacks take place.
"Our officers sacrifice so much for all of us and we need to make sure that if criminals attack them, that we as a city provide every legal means possible to make sure we capture their assailants," said L.A. City Councilman Jose Huizar.
The ordinance, which would also raise the maximum award in such cases to $100,000, must come back for a second reading, but it is expected to pass.