Filner said Friday he will undergo two weeks of full-time therapy, a move one City Council member called a "stunt."
"I thought it was a stunt," KSWB-TV, San Diego, quoted councilmember Scott Sherman as saying. "It felt like a reality TV moment. Just a guy trying to cling to power any way he can."
Filner -- who has been under pressure from supporters and opponents to resign -- has been publicly accused by at least seven women of inappropriate sexual contact.
He told reporters at City Hall Friday his "failure to respect women" and the behavior he engaged in "is inexcusable" and he apologized to supporters, the people of San Diego, and "most of all I apologize to the women I have offended."
Filner, a Democrat said he would enter a behavior counseling clinic Aug. 5 and return to his office Aug. 19, and will receive twice-daily briefings on city affairs. After the two-week stay at the clinic, he said he will receive "ongoing regular counseling."
"My focus will be on making sure that I am doing right by this city in terms of being the best mayor I can be and the best person I must be," Filner said.
Calls for his resignation have come from the highest reaches of the Democratic Party but Filner said he would not resign.
"I think he's just sorry he got caught," Sherman said. "If he's really going to deal with his demons he need to do that on his own and let the city get back to taking care of business and quite embarrassing us on a national scale."
Council President Todd Gloria said in a statement, "The mayor has finally acknowledged his very serious disorder, which prevents his ability to govern and seriously affects his ability to interact with people."
Councilmembers Lori Zapf, Kevin Faulconer, Mark Kersey and Sherrie Lightener also called for Filner's resignation after his announcement.
Four more women, including a university dean and a retired Navy rear admiral, Thursday accused Filner of sexual harassment. All four said in interviews with KPBS-TV, San Diego, Filner should leave office.
Veronica "Ronne" Froman, who retired from the Navy in 2001 and served as San Diego's chief operating officer during a previous administration, described an encounter in which she said Filner backed her into a corner and asked her if there was a man in her life.
"I was really rattled," she said. "I got in the car with the two guys I was working with and I told them never to leave me alone in a room with Bob Filner again."
Joyce Gattas, who helped write the sexual harassment policy at San Diego State University as dean of the College of Professional Studies and Fine Arts, described inappropriate touching and kisses on the cheek.
Sharon Bernie-Cloward, president of the San Diego Port Tenants Association, described an encounter with Filner while he was a member of the U.S. House of Representatives. She said after another encounter while he was running for mayor, she was worried enough about his behavior -- which included grabbing her rear end -- that she got someone to escort her to her car.
Patti Roscoe, a businesswoman, said she has known Filner since he was on the City Council and had a lot of experience with "the famous headlock" and other inappropriate conduct.
One of the women who have come forward this week to tell of Filner's conduct toward them, Irene McCormack Jackson, Filner's former communications director, has filed a sexual harassment lawsuit.
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