Mr. Rudin seeks to have the Alabama lawsuit dismissed. He is also asking for the New York court to declare that the play does not violate his agreement with Ms. Lee and that Ms. Carter does not have the authority to act on behalf of Ms. Lee’s estate. He is demanding that the estate award him damages “in no event less than $10 million.”

“The Agreement did not give Ms. Lee approval rights over the script of the Play, much less did it give her a right to purport to edit individual lines of dialogue,” he argued in the lawsuit. “It certainly did not give such rights to Ms. Carter, who is not an author, editor, literary agent or critic, and has no known expertise whatsoever in theater or writing.”

Ms. Carter emerged as a polarizing figure in the final years of Ms. Lee’s life, as a debate raged over whether or not Ms. Lee had authorized the publication of her second novel, “Go Set a Watchman,” which she had written in the 1950s and had abandoned. Ms. Carter initially said she stumbled upon the manuscript in a safe deposit box in 2014, but a conflicting account suggested the novel had been discovered years earlier.

In a statement Monday, Ms. Carter said, “As the personal representative of the Estate of Nelle Harper Lee, I must protect the integrity of her beloved American classic, and therefore had no choice but to file a lawsuit against Rudinplay for failing to honor its contract with Ms. Lee. It is my duty and privilege to defend the terms of Ms. Lee’s agreement with Rudinplay, and I am determined to do so.”

But, in his lawsuit, Mr. Rudin questioned Ms. Carter’s status as a representative of Ms. Lee’s will and for the first time accused Ms. Carter of having an ulterior motive in challenging the play: a desire to force the cancellation of the Broadway production because of a separate dispute between Ms. Lee’s estate and the heirs of Gregory Peck, who played Atticus Finch in the movie adaptation, over stage rights.

While a local theater group in Ms. Lee’s hometown Monroeville, Ala., has staged a production based on the novel annually for nearly three decades, there has never been a Broadway adaptation of “Mockingbird,” one of the most beloved novels in American literature. In the lawsuit, Mr. Rudin suggests he already intends to postpone the new production, writing that the legal dispute “has rendered it impossible for the play to premiere as scheduled in December, 2018, and unless this dispute is resolved in the immediate future, the play will be canceled.”

In an interview, Mr. Rudin said he was willing to take the unusual step of performing the play in a courtroom so a jury could determine whether or not the production is true to the spirit of the novel. “A play and a book are two different things. A book is meant to be read; a play is meant to be performed,” he said.