When he was sacked, three faculty committees accused him of plagiarism, fabrication and other research misconduct.
Churchill has denied the allegations and called the investigation “a farce” and “a fraud”.
Churchill’s controversial view was written in an essay which compared some World Trade Center victims to Adolf Eichmann, the Holocaust organiser.
However, the university’s leaders said his dismissal was because of other writing unrelated to his September 11 comments.
Ken McConnellogue, a university spokesman, said the school stood behind the regents’ vote.
“We believe this is a matter of academic integrity for the university, so we will not be settling the lawsuit,” he said.
David Lane, Churchill’s lawyer, said earlier that reinstatement was “definitely on the table” if Churchill wins his case.
The suit claims that both the academic investigation and the decision to fire Churchill were retaliation. It also says Churchill’s right to due process under the US and state constitutions was violated and accuses the university of breach of contract.
The essay that thrust Churchill into the national spotlight was titled Some People Push Back: On the Justice of Roosting Chickens.
The essay and a follow-up book argued that the September 11, 2001, attacks were a response to a long history of US abuses.