The move by the publishing company is only the latest legal controversy to erupt over the play since Mr. Rudin persuaded Ms. Lee, shortly before her death, to grant him the rights to create a Broadway adaptation of her novel and to permit the screenwriter Aaron Sorkin to write the script. Last year the Lee estate sued Mr. Rudin, asserting that a draft script deviated impermissibly from the novel; Mr. Rudin countersued, and the case was settled.

The latest dispute, over whether and when the Sergel adaptation can be staged now that the Sorkin adaptation exists, pits an agreement Ms. Lee signed with Dramatic Publishing in 1969 against one she signed with Mr. Rudin in 2015.

The disagreement broke into public view in January, when a British production company announced that it was canceling a planned tour of the Sergel production under threat from Mr. Rudin’s lawyers. Then last month, eight American theaters separately said they were canceling productions of the play for the same reason.

The cancellations, some of them at small, volunteer-run theaters, and in some cases just before the start of planned productions, prompted an outcry. Mr. Rudin then said he would allow the affected theaters to stage the Sorkin production, rather than the Sergel production, an offer that came too late for some, but was enticing to others.