A spokesman for Attorney General Kamala Harris said "an investigation is under way" into accusations Filner had inappropriate contact with a number of women, U-T San Diego reported Friday.
Filner resigned Friday after three days of mediation, but that action has no effect on any possible criminal action.
Filner apologized to the city after his resignation was announced, but insisted a "lynch mob" mentality had led to his departure.
"The city should not have been put through this, and my own personal failures were responsible," Filner said in city council chambers.
Filner said he meant only to establish personal relationships, "but the combination of awkwardness and hubris I think led to behavior that many found offensive."
"Not one allegation ... has even been independently verified or proven in court," he added. "But the hysteria that has been created is the hysteria of a lynch mob."
City Council President Todd Gloria will serve as interim mayor.