Democrat Bob Filner stood aside with an apology to the women concerned, but denied harassing anyone.
Bob Filner’s departure follows a deal with the Californian city’s council over legal fees for the lawsuit he faces.
City Council President Todd Gloria will now become acting mayor and a special election will be held in 90 days.
“The city should not have to go through this, and my own personal failures were responsible and I apologize to the city,” the 70-year-old Bob Filner told a special meeting of the San Diego city council on Friday.
“To all the women that I’ve offended, I had no intention to be offensive, to violate any physical or emotional space,” he added.
“I was trying to establish personal relationships, but the combination of awkwardness and hubris led to behavior that I think many found offensive.”
But he struck a defiant tone as he added: “Not one of the allegations has ever been independently verified or proven in court.
“I’ve never s***ally harassed anyone.”
He said he had been the victim of “the hysteria of a lynch mob”.
Under Bob Filner’s resignation deal, the city will pay his legal fees in a joint defense of a lawsuit filed by the mayor’s former communications director, said City Attorney Jan Goldsmith.
It will also pay for any settlement costs against the mayor except for punitive damages. The city would also pay up to $98,000 if Bob Filner wants to appoint his own lawyer.
He also faces a criminal investigation, the California attorney general’s office said on Friday.
Bob Filner’s former spokeswoman, Irene McCormack Jackson, was the first to accuse him publicly of inappropriate behavior. She launched a lawsuit last month against him and the city.
Irene McCormack Jackson alleged that the mayor had asked her to work without underwear, demanded kisses and told her he wanted to see her without clothes.
Her lawyer, Gloria Allred, told reporters: “It is not appropriate for the city of San Diego to provide a gift of public funds to a s***al harasser to help him fight the victim of the lawsuit we filed.”
She also said she strongly supported the mayor’s resignation.
Since the lawsuit, a series of women, including high-profile city residents and a great-grandmother, have come forward with accusations against Bob Filner.
Veronica Froman, a retired rear admiral, said Bob Filner once blocked her from leaving a room, ran his finger up her cheek and asked if she had a man in her life.
The president of the city port tenants’ association, Sharon Bernie-Cloward, said Bob Filner had groped her on her bottom at an event last year.
“I was left there startled and fearful,” she was quoted as saying by US media.
“I actually had someone walk me to my car that night.”
Other alleged victims included several businesswomen, a college dean and two military veterans who said he harassed them as they attended a meeting for women who had been raped while serving in the armed forces.
Bob Filner initially resisted pressure to quit, submitting himself instead to undergo two weeks of behavioral therapy.
But as allegations continued to stack up, pressure for Bob Filner to go mounted, including from both US senators for California and the national head of the Democratic National Committee.
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