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In the aftermath of a right-wing rally Sunday that ended with anarchists chasing attendees from a downtown park, Berkeley Mayor Jesse Arreguin urged UC Berkeley on Monday to cancel conservatives’ plans for a Free Speech Week next month to avoid making the city the center of more violent unrest.

“I don’t want Berkeley being used as a punching bag,” said Arreguin, whose city has been the site of several showdowns this year between, on the one hand, the left and its fringe anarchist wing, and on the other, supporters of President Trump who at times have included white nationalists.

“I am concerned about these groups using large protests to create mayhem,” Arreguin said. “It’s something we have seen in Oakland and in Berkeley.”

The mayor wants UC Berkeley to halt plans by a conservative campus group, the Berkeley Patriot, to host right-wing provocateur Milo Yiannopoulos during its scheduled Free Speech Week from Sept. 24-27. Berkeley’s right-vs.-left cage matches began with an appearance that Yiannopoulos was to have made in February at a campus hall, an event that was aborted when black-clad anarchists like those who broke up Sunday’s downtown rally stormed into Sproul Plaza, smashed windows and set bonfires.

Trump himself denounced UC Berkeley in a tweet the next day, and his supporters have since made a point of bringing their fight to the famously liberal college town.

There have been reports that the Berkeley Patriot is also trying to lure ousted White House chief strategist Steve Bannon and right-wing commentator Ann Coulter to appear on campus during its Free Speech Week. Bryce Kasamoto, a spokesman for the group, said Monday, “We are still working out the logistics of this event with the university and law enforcement. Once we have worked out final specifics, we will be able to confirm speakers for Free Speech Week.”

Arreguin is wary of the whole idea.

“I’m very concerned about Milo Yiannopoulos and Ann Coulter and some of these other right-wing speakers coming to the Berkeley campus, because it’s just a target for black bloc to come out and commit mayhem on the Berkeley campus and have that potentially spill out on the street,” Arreguin said, referring to militants who have also been called anti-fascists or antifa.

The anti-Yiannopoulos protesters inflicted $100,000 worth of damage to the school’s student union in February before taking to the streets of Berkeley, where several businesses’ windows were smashed. Arreguin said inviting the former Breitbart News editor and other right-wing speakers was setting up a possible repeat of that destruction.

“I obviously believe in freedom of speech, but there is a line between freedom of speech and then posing a risk to public safety,” the mayor said. “That is where we have to really be very careful — that while protecting people’s free-speech rights, we are not putting our citizens in a potentially dangerous situation and costing the city hundreds of thousands of dollars fixing the windows of businesses.”

UC Berkeley spokesman Dan Mogulof said the university is working with the Berkeley Patriot to come up with a time and location for Yiannopoulos’ appearance. He emphasized that UC Berkeley wasn’t the one extending the invitation, but that “we have neither the legal right nor ability to interfere with or cancel (students groups’) invitations based on the perspectives and beliefs of the speakers.”

“Where we do have discretion is around everything that has to do with the safety of our communities, and the well-being of those who may feel threatened or harmed by what some of these speakers may espouse,” Mogulof said. “We can assure you that those priorities, along with our commitment to free speech, remain at the center of our planning and priorities.”

Also on tap for next month is a campus appearance by Ben Shapiro, another former Breitbart News editor, who is scheduled to speak Sept. 14 at the 1,900-capacity Zellerbach Hall. His appearance is sponsored by Berkeley College Republicans.

Shapiro told The Chronicle last week that he would welcome anyone who wanted to protest his appearance, but that “I’m actively telling people not to show up to defend my free speech. That’s the police’s job.”

UC Berkeley is charging the organizers of Shapiro’s appearance $15,000 for the campus’ security costs.

San Francisco Chronicle columnists Phillip Matier and Andrew Ross appear Sundays, Mondays and Wednesdays. Matier can be seen on the KPIX TV morning and evening news. He can also be heard on KCBS radio Monday through Friday at 7:50 a.m. and 5:50 p.m. Got a tip? Call (415) 777-8815, or email matierandross@sfchronicle.com. Twitter: @matierandross