The special election is estimated to cost the city up to $7.65 million, according to the City Clerk's Office. A runoff, if necessary, will take place on June 27.
Council President Paul Krekorian said the funding would be discussed further in the Budget and Finance Committee. The ordinance will come before the council next week for final consideration.
The Sixth District — which includes central and eastern portions of the San Fernando Valley — is being overseen by a non-voting caretaker, the city's chief legislative analyst, Sharon Tso. A non-voting caretaker does not hold a seat on the council, but oversees the council office to make sure the district provides constituent services and other basic functions.
The last day for interested candidates to file a declaration of intent is Dec. 12, according to the ordinance.
Martinez resigned after she uttered several racial slurs in an October 2021 leaked conversation about city redistricting. Her term was set to expire in December 2024.
The other two council members involved in the leaked conversation that spurred the scandal, Kevin de León and Gil Cedillo, have so far defied calls to resign.
De León's term also expires in December 2024.
Cedillo lost his re-election bid to Eunessis Hernandez in June and will leave office in December. Krekorian has suggested swearing in Hernandez immediately if Cedillo resigns.
After ejecting several protesters from the chamber Wednesday who were asking the council not to meet unless the pair both step down, Krekorian said ahead of the vote that this item was an example of why it was important for the council to keep meeting.
"A quarter of Angelenos who are now deprived of representation because of the resignation of Ms. Martinez would be left without representation," he said. "I think it just emphasizes the importance that the council continues to meet in order to respond to the very crisis that was created — that so many members of the public are talking about and with whom we stand in solidarity."
PREVIOUS COVERAGE: Kevin de León recall effort launched amid City Hall racism scandal
Recently, Councilwoman Heather Hutt served as non-voting caretaker of the 10th District for several months before being appointed as council member last month in place of Mark Ridley-Thomas, who is suspended as he awaits trial on federal corruption charges. Previous fill-in Councilman Herb Wesson was legally barred from serving on the council.
In the leaked 2021 recording, Martinez and her colleagues discussed appointing Hutt to the seat, claiming that Hutt would support them.
Hutt, in a statement after the tapes were leaked, said she was not aware of the conversation before she was appointed and claimed she was "not a pawn."
"The way they talked about the appointment process has sullied the appointment process, so if there's any way to prevent us from having to go through that again, I think we do that," Councilman Marqueece Harris-Dawson told City News Service after Martinez's resignation. "The best way is to go directly to the voters."