Capt. Alex Yao of the University of California Police Department says authorities have received intelligence that protest groups could turn up throughout the day and into the night.
He said Wednesday that police would have a "very, very low tolerance for any violence."
He also said that Berkeley campus police have briefed local and state police departments on their concerns of violence and to let them know they might be called on for assistance.
Berkeley's reputation as one of the country's most liberal universities, in one of America's most liberal cities, has made it a flashpoint for the nation's political divisions in the era of Donald Trump.
Troy Warden, the student group's president, says College Republicans "had to cancel the event out of concern for the safety of students."
Warden made the comments Wednesday in a news conference on UC Berkeley's campus.
UC Berkeley officials had said they were unable to provide a safe place for Coulter's proposed Thursday event, amid concerns of violent protests. The university had instead offered to let her speak on May 2.
Coulter's student backers say the university is biased against conservative speakers and violating her right to free speech.
The conservative pundit has hinted she might cancel her planned appearance Thursday amid growing concerns of violence. She told Florida-based radio station 850 WFTL on Wednesday, "I still wanted to do it but I'm running out of options here."
Campus spokesman Dan Mogulof said UC Berkeley officials had not heard directly from Coulter on Wednesday. But he said even if she cancels, some groups that support or oppose her could still turn out on campus.
He said police were taking necessary steps to protect the campus but he declined to elaborate.
Campus Republicans invited Coulter to speak at the campus. They did not immediately respond to requests for comment.