Voters will be asked to consider amending the city charter to guarantee that the library department receives a larger share of the city's property tax revenue for its annual operating budget.
The budget cuts have forced the layoffs of more than 100 library staffers.
Councilman Bernard Parks, a former police chief, proposed the measure, saying "libraries are probably our best crime prevention dollars."
City Council President Eric Garcetti agreed.
"Libraries are a proven and cost-effective way to improve our economy and keep our youth on the right track, and this measure supports libraries with no increased cost to the taxpayers," he said.
City Librarian Martin Gomez said if the measure were approved it would restore the department's budget to 2009-10 levels, enough to keep all of the city's 73 libraries open at least six days a week, four evenings per week. Nine locations would also remain open on Sundays.
City News Service contributed to this report.