Cook County Board President Toni Preckwinkle said Thursday that she was “profoundly discouraged and appalled by the behavior of my chief of staff” — as questions about whether Preckwinkle acted swiftly enough to fire John Keller drew more sparks in the mayoral race.

New rival mayoral candidate Susana Mendoza criticized Preckwinkle’s response to the sexual harassment allegations, saying she was “pretty horrified” to learn that Preckwinkle waited until just a few days before announcing her own run for mayor to act on the allegations.

“As a woman, I was pretty horrified by that. As a woman, especially, who’s been fighting the issue of sexual harassment for the last year of my life and trying to do the best to elevate women — not just into politics, but into safe work environments,” Mendoza told the Chicago Sun-Times.

But Preckwinkle defended her handling of the matter in an unrelated news conference after Thursday’s Cook County Board meeting and in a statement issued later. She said she has assembled a “group of experts to advise my Administration” on handling harassment questions in cases where little information is provided about the potential wrongdoing.

“This is something I take really, really seriously as a woman, as a mother, as a grandmother as somebody who was a teacher for 10 years and tried to instill in my students respect for themselves and respect for others,” Preckwinkle told reporters.

“I’ve been in government and public life for 30 years and I’ve experienced … unwanted advances and inappropriate behavior and I don’t want any woman put in that position, nor do I want them to be afraid to come forward.”

Preckwinkle demanded Keller’s resignation in mid-September for “inappropriate and disrespectful behavior.”

At the time, the Hyde Park Democrat insisted she had no prior knowledge of any harassment or sexual abuse issues involving her chief of staff before she decided to fire him.

But questions have surfaced about how much Preckwinkle knew and when she knew it.

After a Chicago Tribune report last week, Preckwinkle admitted she knew of an ” an unsubstantiated rumor” that Keller had acted in an inappropriate manner as early as March.

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“No victim came forward, and there was nothing I could act on,” Preckwinkle said in a statement, explaining why she didn’t act sooner. “In September, I received an allegation that was corroborated, and I acted immediately.”

Mendoza, who was re-elected state comptroller last week, is not the first mayoral candidate to criticize Preckwinkle’s handling of the matter. Lori Lightfoot said Preckwinkle’s actions on Keller indicate a “toxic culture” and the city needs “leaders who will reject this culture and instead build a transparent and accountable City Hall that serves the people, not the broken political machine.”

Mendoza was asked whether she believes Preckwinkle participated in a political cover-up.

“You’d have to ask her. I don’t know all of the details. I’m just telling you that I was disappointed as a woman. As someone who really believes the issue of sexual harassment is front-and-center, especially right now,” Mendoza said.

Earlier this year, after harassment scandals within his organization, House Speaker Michael Madigan named Mendoza and two other Democratic women to lead a statewide discussion about the role of women in the Democratic party and how to “change the culture of politics.”

“We’re finally at a place where women can come forward. And they should be believed. … I’ve been very clear where I stand on the issue of sexual harassment and on the need to believe women who come forward about their allegations and really thoroughly investigate and look into that stuff.”

Preckwinkle maintained that she asked the person who brought the original rumor to her to corroborate it and, when that didn’t happen, she could take no further action against Keller. But as soon as a victim came forward with a credible allegation, she said she acted, firing Keller a few days later.

“I discipline people and I fire people on the basis of evidence,” Preckwinkle said. “When I had evidence, corroboration of his bad behavior, I fired him. I deeply regret his behavior.”

After Mendoza’s remarks, Preckwinkle issued a statement, repeating that she doesn’t fire or discipline employees based on rumor.

“Let me be clear, only one incident came to my attention,” Preckwinkle said. “It was brought to me on Friday, September 14, quickly substantiated and I fired my Chief of Staff on Tuesday, September 18th. My priority has always been the victim and I respect her request for anonymity and privacy.

“Separately, back in March, a third-party rumor about inappropriate conduct by John were (sic) relayed to me. I took this seriously, confronted my Chief of Staff and urged any potential victim or witness to come forward or make a report. No other details or individuals ever came forward. I’ve never disciplined or fired anyone based on a rumor. I’ve done so on the basis of fact.

“As President of the second largest county in the country, it’s my responsibility to not only react to incidents but work to shape a positive, inclusive work environment. That’s why I have assembled a working group of experts to advise my Administration on what can and should be done in situations like this, when there is no incident, details or a specific victim that comes forward.

“I encourage anyone who has been harassed, abused, and assaulted to come forward.”