Coulter, one of America's best-known and most provocative pundits on the political right, said on Wednesday that she no longer intended to defy university officials by addressing UC Berkeley students on campus this week.
But Coulter left open the possibility of paying a visit to her supporters at the school, long a bastion of liberal student activism and a center of the Free Speech Movement protests of the 1960s.
UC Berkeley officials said classes would be held as scheduled.
But campus police Captain Alex Yao told a news conference late on Wednesday that his department would maintain "a highly visible presence" on Thursday, pointing to continued threats of violent protests.
"Many of the individuals and organizations which planned to protest Ann Coulter's appearance or support it still intend to come to campus," university spokesman Dan Mogul of told news agency Reuters.
Indeed, social media feeds of left-wing and right-wing activists remained abuzz with vows to proceed with demonstrations and counter-demonstrations over the Coulter-Berkeley controversy.
In February, protesters opposed to an appearance by Milo Yiannopoulos, then a senior editor for the conservative Breitbart news website, set fires, broke windows and clashed with police on campus, prompting cancellation of his speech.
And in March and again in April, opposing groups from the far-right and far-left skirmished violently near campus.
All three incidents were cited on Wednesday in an open letter from UC Berkeley Chancellor Nicholas Dirks explaining the school's position.
University officials said the Berkeley College Republicans erred by inviting Coulter without notifying campus officials in advance, as is required of all student groups, and by failing to submit to a "security assessment" to determine a suitable time and place for the event.
UC Berkeley officials denied that Coulter was unwelcome because of her politics.
After initially barring her from speaking on campus on Thursday, university officials proposed moving her appearance to next Tuesday. Coulter said she could not make it then and accused the school of trying to limit her audience by choosing a date that fell in a study week ahead of final exams.
Coulter then insisted publicly that she would go through with her speech on Thursday, over the university's objections. But she said she changed her mind after student organizers withdrew their invitation, though they vowed to press ahead with a lawsuit filed on Tuesday accusing UC Berkeley of suppressing freedom of speech.