More than a dozen women have publicly accused Filner, a Democrat, of making inappropriate statements or sexual advances. The 70-year-old former congressman has resisted numerous calls to resign.
He is set to return to work this week after undergoing behavior therapy.
"He is a sexual predator. He has abused the power of his office," said Rachel Laing, spokeswoman for the recall campaign. "He can't possibly lead or possibly reclaim his ability to lead."
Recall organizers say they have raised more than $100,000 so far and more than 1,100 people have signed up to volunteer. They sought out signatures at a half-marathon Sunday in Balboa Park, while businesswomen and military sexual-assault victims planned to lead an afternoon march downtown.
House Minority Leader Nancy Pelosi has said Filner should step aside and spare San Diego the pain and expense of a recall election.
The latest accusation against Filner came Thursday, when a volunteer city worker who assists senior citizens said the mayor repeatedly rubbed her hands, asked her on dates and made sexually suggestive comments.
The recall petitions include Filner's response, filed Monday with the city clerk, in which he tells voters this is "not the time to go backwards" and touts his administration's job-producing projects and quality of life initiatives, like removing cars from Balboa Park and proposing that the 2024 Olympic Games be held in San Diego and Tijuana.
Filner made no mention of the allegations against him in his response. He has said in the past that he has disrespected women but has denied being guilty of sexual harassment.
The recall effort must collect 101,597 signatures of registered San Diego voters by Sept. 26. If the petition has fewer than that, the recall campaign will have 30 more days to circulate a supplemental petition to gather additional valid signatures.
If enough signatures are validated by the city clerk, the petition will be presented to the City Council, which must schedule an election within 60 to 90 days.
Filner has stayed out of sight, but his lawyers said he completed two weeks of intensive behavior therapy.
Earlier this month, Democratic Sen. Barbara Boxer sent a letter to Filner, urging him to step down from office.
"You have betrayed the trust of the women you have victimized, the San Diegans you represent and the people you have worked with throughout your decades in public life," she wrote.