"Words alone are not enough," Filner said at a nationally televised news conference. "I am responsible for my conduct and I must take responsibility for my conduct so that such conduct does not ever happen again."
Filner said he will receive twice-a-day briefings about city operations while participating full-time in what he described as "intensive therapy" beginning Aug. 5. He said more counseling would follow.
Filner, who is 70 and divorced, did not take any questions after the announcement that was briefly interrupted by a microphone problem.
Several people who have called on Filner to resign said his plan for therapy was inadequate. They reiterated calls for the Democrat to step down.
"Two weeks of therapy may help Bob Filner with his personal problems, but it does not help to address the needs of San Diego," said Laura Fink, a political consultant who alleges that Filner patted her buttocks at a 2005 fundraiser when she was deputy campaign manager for the then-congressman.
Kevin Faulconer, a Republican city councilman, said Filner's "bad behavior" will not end after two weeks of therapy.
"Bob Filner should leave to receive the help he obviously needs, but he shouldn't take the office of the mayor and San Diego city government with him." Faulconer said. "He needs to resign and seek long-term treatment as a private citizen."
Another Republican city councilwoman, Lorie Zapf, said Filner's refusal to step down was "an insult to women everywhere."
When the allegations first surfaced two weeks ago, Filner apologized for disrespecting women and said he needed help. But soon after, he said he was innocent of sexual harassment and resisted calls to leave office.
The former congressman is San Diego's first Democratic mayor in 20 years, and he is less than eight months into a four-year term.
The chairwoman of the Democratic National Committee called on Filner to resign as did leaders of the San Diego Democratic party after seven women identified themselves as targets of his sexual harassment. Some of the claims included unwanted touching.
The mayor spoke a day after the latest accusers came forward, including a retired Navy rear admiral and a dean at San Diego State University.
Democratic National Committee Chairwoman Debbie Wasserman called Filner's alleged behavior "reprehensible and indefensible" while urging him to step down.
A week ago, the local Democratic committee deadlocked 24-24 on the question, but that vote was before any woman had publicly identified themselves as a target.
After the vote on Thursday, Francine Busby, the county party chairwoman, said, "We are not here to determine guilt or innocence. However, in the best interest of the city, the San Diego County Democratic Party has voted to ask Mayor Filner to step down, seek the personal help that he needs, and allow San Diego to move forward."
Fink welcomed the party's position but expressed doubt at the time that Filner would resign.
"Bob Filner is one of the most stubborn people I have ever met," she said. "I see him holding on tightly to the grip of the mayor's office."
Veronica "Ronne" Froman, the retired rear admiral, said Filner once blocked a doorway after others left a meeting, ran his finger up her cheek and asked if she had a man in her life.
Froman, who is known in San Diego as the "Navy Mayor" and has led the American Red Cross local chapter, said the incident occurred a couple years ago at Filner's congressional office.
Sharon Bernie-Cloward, president of the San Diego Port Tenants Association, said the then-congressman told her at an event in 2010 that she was beautiful and he wanted to date her after his re-election. At another event last year during the mayoral campaign, she said Filner "groped me on my backside inappropriately."
"I was left there startled and fearful. In fact, I actually had someone walk me to my car that night," she said.
Patti Roscoe, a businesswoman in the tourism and hospitality industry who knew Filner before he was elected to Congress in 1992, said Filner placed her in a "headlock" numerous times and tried to kiss her on the lips.
"I'd have to squirm to get away. And just as recently as a few months ago this happened. I turned and he just slobbered down my chin," Roscoe said.
On Monday, the mayor's communications director from January to June, Irene McCormack Jackson, filed a lawsuit claiming that he asked her to work without panties, demanded kisses, told her he wanted to see her naked and dragged her in a headlock while whispering in her ear.