(CNN) -- Dogged by allegations of sexual harassment, San Diego Mayor Bob Filner admitted Thursday "that I need help" but stopped short of resigning.
"I'm clearly doing something wrong," he said.
Some of his longtime backers are urging Filner to step down. Among them is former city councilwoman Donna Frye -- a Democrat, like Filner, who recently worked in the mayor's office. She said Thursday that after hearing allegations directly from several women, "I could not not act." She sent Filner a letter Tuesday asking him to step down.
Filner acknowledged Frye's request in a statement Thursday and implicitly admitted there was merit to her concerns.
"I am embarrassed to admit that I have failed to fully respect the women who work for me and with me, and that at times I have intimidated them," he said. "It's a good thing that behavior that would have been tolerated in the past is being called out in this generation for what it is: inappropriate and wrong."
No women have come forward publicly to detail allegations against Filner. He has not been charged with any crime, nor has anyone filed a lawsuit against him.
Yet Marco Gonzalez, a Southern California lawyer, told reporters Thursday he and Frye know of "very specific acts from individuals who have worked for the mayor that they have been subjected to behavior that does not meet our community standards." It's up to them to provide specifics, Gonzalez said, but even absent such public declarations, he and others felt compelled to speak out for them.
"I believe what they have told me, and they are not alone," Frye said.
Amid the uproar, the mayor announced Thursday that he's "begun to work with professionals to make changes in my behavior and approach" and that he and his staff will have sexual harassment training. Filner also promised that he'd personally reach out and apologize to those who now or have in the past worked in his office.
"Please know that I fully understand that only I am the one that can make these changes," he said.
Filner did not indicate he had any plans to resign.
Earlier this week, numerous reports -- including one from CNN affiliate KSWB -- said that Filner's fiancee, Bronwyn Ingram, had called off their engagement for unspecified reasons.
The Republican Party of San Diego cheered Ingram's move on its Facebook page, saying "she deserves better." Since then, they have kept up their criticism of Filner and Democrats who, they allege, overlooked Filner's behavior that they claim "has been widely known ... for years."
In her remarks Thursday, Frye said she understood that "there will be many opportunities to turn this into a political side show or worse." The mayor himself can help address the crisis, and help San Diego, by stepping down, she said.
"I am asking our mayor and his closest advisers to please take this to heart," the councilwoman said. "To please hear what we are saying, and to do the right thing."