The University of California regent who was recorded last year asking an actress at his podcast company if he could hold her breasts said Friday he’s considering resigning amid calls for him to step down from the powerful panel.

But Regent Norman Pattiz told The Chronicle that if he does resign, it won’t be because of demands that he do so.

“Had this (recording) not come up, I might have considered retirement more than I’m considering it now,” Pattiz said, noting that he’ll be 75 next month and has been a regent for 16 years. “I certainly don’t like the idea of retiring under a cloud.”

Pattiz, who has apologized for his remarks and said they were meant as a joke, said he hasn’t yet decided whether to step down.

“I haven’t made that determination,” he said. “If I become a distraction, I don’t want that. I care too much about the university. Time will tell if I’m going to be a continuing distraction.”

Now, as the UC student government and student protesters demand that Pattiz resign, Lt. Gov. Gavin Newsom and two other regents are raising questions about whether the Board of Regents has dealt too lightly with their colleague while cracking down on sexual harassment elsewhere in the university.

In addition, a UC labor union has proposed a constitutional amendment to give the Legislature authority to remove a regent.

“Unfortunately, while California’s Constitution gives the governor the power to appoint regents to 12-year terms, there is no provision granting authority to remove regents,” Kathryn Lybarger, president of the American Federation of State, County and Municipal Employees, said in a statement. “Inaction cannot be the solution.”

The state Constitution allows the governor to appoint 18 of the 26 UC regents to 12-year terms. The remaining eight regents — including the governor, lieutenant governor, state schools chief, a UC student and other officeholders — serve automatically while in office.

The controversy over Pattiz came to light in October 2016, when actress Heather McDonald posted the recording of him on her “Juicy Scoop” podcast, which by then was no longer hosted by Podcast One, Pattiz’s Los Angeles company.

McDonald had been recording ads for her podcast when Pattiz knocked on her studio door. Listeners can hear Pattiz calling out that her show is becoming more popular. McDonald asks Pattiz to let her finish the ad. As she begins touting the product, a brassiere made of memory foam, she gets flustered and stumbles on the words.

“You’re making me nervous now,” she tells Pattiz. “Let me do one more.”

Pattiz says: “Wait a minute. Can I hold your breasts?”

“No,” McDonald says.

“Would that help?” Pattiz says, adding that his hands “are memory foam.”

McDonald said she often felt uncomfortable during her weekly visits to the recording studio because Pattiz repeatedly commented on her appearance or joked about following her into the restroom.

Pattiz has denied creating a hostile work environment.

A year later, as growing numbers of women have been speaking out about sexual harassment and the issue has become acknowledged as intolerable, the incident has resurfaced.

On Nov. 29, three regents asked UC President Janet Napolitano and regents Chairman George Kieffer what they have done to discipline and investigate Pattiz.

“This has been a matter of deep concern at many levels of the UC, especially in light of the systemwide work we have done to address sexual harassment and sexual violence,” wrote Newsom, state schools chief Tom Torlakson and student Regent Paul Monge.

Kieffer responded that Pattiz was neither investigated nor disciplined because he wasn’t on university business when he made his statements to the actress. Kieffer reiterated that the regents have since changed the policy so that outside misconduct can trigger an investigation.

Kieffer added that McDonald never filed a complaint with the regents. And he said that since the incident, the regents have been required to undergo the same anti-sexual-harassment training that’s required of UC employees.

The letter from the three regents mentioned the November regents meeting, when dozens of UC Berkeley students protested against Pattiz.

“Students have made it clear that they do not feel comfortable with Mr. Pattiz serving and representing (them) on the UC Board of Regents,” the regents wrote, adding that the UC Student Association approved a resolution in January calling on Pattiz to step down. (The students approved a second, updated resolution in October. Both call the regents hypocritical for disciplining UC employees for sexual harassment but not their colleague.)

The regents’ letter also cited a lawsuit against Pattiz filed in September by a former producer at Podcast One who accused Pattiz of brandishing a gun and retaliating against him for giving the harassment recording to McDonald.

Finally, the letter criticized Pattiz for telling the San Jose Mercury News that student protesters “ought to be ashamed of themselves.”

Pattiz has denied the allegations in the lawsuit. He said Friday that when he said the students should be ashamed, he was referring to the UC Student Association’s resolutions against him “because (they’re) full of information that isn’t true,” such as referring to “multiple cases of sexual harassment.”

Asked for evidence of additional sexual harassment accusations against Pattiz, UC Student Association President Judith Gutierrez said she was looking into it.

Meanwhile, in February, Pattiz will resign from his key role as chairman of the Boards of Governors for the Lawrence Livermore and Alamo national laboratories, which are run by UC.

Ellen Tauscher, a former congresswoman who represented the East Bay and became a regent in June, will take over as lab chairwoman on Feb. 16. Tauscher was undersecretary of state for arms control and international security affairs under President Barack Obama, among other high-security roles in federal government.

Nanette Asimov is a San Francisco Chronicle staff writer. Email: nasimov@sfchronicle.com Twitter: @NanetteAsimov