A university spokesman says the school values the amendment but the group organizing the speaking engagement didn't follow proper procedure.
Police say there were security concerns over the conservative commentator's planned event, and even though she won't be on campus, they still are planning for possible violence.
Coulter's plan to speak created a war of words on the traditionally liberal campus roiled by recent protests.
Coulter took to her verified Twitter account Wednesday to say the university canceled her speech, but UC Berkeley said it had never been officially scheduled.
University spokesman Dan Mogulof said: "Ms. Coulter and speakers regardless of their position are welcome on this campus."
But an attorney for the Berkeley College Republicans
and Young America's Foundation
told reporters that the university was denying conservative groups their rights. The lawyer said the school told her it wouldn't provide a room for the event.
"The First Amendment requires equal access, not one level of open access for conservatives, out in the open, with attackers shouting us down," lawyer Harmeet Dhillon said, "and another level of access in a private, closed setting where people are allowed to enjoy an educational opportunity without interruption."
Coulter tweeted several statements, saying it was the school that canceled the event.
"It's sickening when a radical thuggish institution like Berkeley can so easily snuff out the cherished American right to free speech," she wrote on her verified account.
Troy Worden, president of the Berkeley College Republicans, said at an outdoor news conference that the university didn't provide a venue.
"In effect, our free speech has been stifled because the university has decided not to assist us in making sure the event can occur successfully," he said as protesters shouted nearby. "We aren't going to have a dangerous event."
He blamed the university and campus police, who have cited credible threats against Coulter and others connected with announced event.
The Berkeley College Republicans and Young America's Foundation are suing the university, accusing
the school of discriminating against conservative guest speakers by placing onerous time and location restrictions on their appearances. "A lawsuit is a long-term remedy that is going to affect not just Ann Coulter's speech but other speakers at UC Berkeley," Dhillon told reporters. "The goal is much larger than Ann Coulter's speech here tomorrow."
The university had no comment on the lawsuit, Mogulof said.
Berkeley, known for decades as a bastion of free speech, has seen protests turn violent in recent months.
Earlier this month, 21 people were arrested
when anti-Trump and pro-Trump groups clashed in a city park.
In early March, 10 people were arrested when pro- and anti-Trump groups fought in Berkeley.
In February people took to the streets to protest an appearance by right-wing commentator Milo Yiannopoulos. The university said more than $100,000
in damage was done.
University police Capt. Alex Yao said authorities have evaluated their response to the February violence and deployment and staffing will be significantly different Thursday. Police will have a highly visible presence, because they believe there still will be protests.
"Tomorrow we are going to have a very, very low tolerance for any sort of violence on campus," Yao said.
School: We did everything we could
Mogulof, the university spokesman, said the school asks for two months notice of an event so it can work out logistics and security. The school was tentatively notified by an email in mid-March that said the group was hoping to get Coulter to appear in late April or in the fall.
No specific date was discussed, he said.
University officials learned of the event being scheduled for April 27 when they read it in a newspaper, he said.
The school scrambled to find a venue, he said.
"We know how to do this but we can't do what we want to do to facilitate those speakers if the groups that want to invite them and host them don't work with us in the way that they need to," he said.
The university suggested May 2 as a date for the event -- but school is not in session that day, so Coulter and the YAF opposed that idea.
Dhillon said the university's security concerns were not enough to prevent the school from providing a venue during a time when students could come to the event. The school provides security at football games where there are issues with drunk people, she said.