Filner -- who was accused Tuesday of sexual harassment by an eighth woman -- had asked the council to cover his legal defense.
Before taking up the request, the council voted unanimously to approve a cross-complaint against Filner, U-T San Diego reported.
"If Bob Filner is engaged in unlawful conduct and the city is held liable, he will have to reimburse us every penny the city pays and its attorney fees," City Attorney Jan Goldsmith said.
KPBS-TV, San Diego, said in a tweet Tuesday its evening news telecast would report new allegations against Filner, 70, bringing to eight the number of women who have publicly alleged he sexually harassment them.
The cross-complaint approved by the council Tuesday stipulates Filner is personally liable for any damages and the city has a "zero tolerance policy as to sexual harassment and sexual harassment is not within the course and scope of employment," the newspaper said.
Filner said last week he will take a two-week leave of absence and undergo therapy beginning Aug. 5.
The City Attorney's Office has served the mayor with a subpoena to testify Aug. 9 at a deposition in its investigation of allegations by former Filner spokeswoman Irene McCormack Jackson. She filed suit last week against Filner and the city, accusing Filner -- a Democrat and a former member of the U.S. House of Representatives -- of creating a hostile work environment and treating women as "sexual objects or stupid idiots."
Seven of the City Council's nine members have asked Filner to resign.
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