Ms. Lee’s estate suffered a setback earlier this week, when a federal court in Alabama agreed with Mr. Rudin that the dispute should be handled in the New York court. Ms. Lee’s estate then sought to delay the trial, which had been scheduled for June, for reasons that it sought to keep secret, according to court documents.

The requests to dismiss both cases filed in federal court in Manhattan on Thursday included no details of the settlement, and it was not immediately clear whether Mr. Rudin had agreed to change the script, or whether the Lee estate was no longer seeking such changes. Among the issues had been whether the depiction of Atticus Finch was sufficiently heroic.

The two sides issued a four-sentence statement saying that they had “amicably settled” the litigation, but offering no specifics. Mr. Rudin declined to comment, and a lawyer representing the estate referred to the joint statement and declined to comment further.

Mr. Rudin is co-producing the play with Lincoln Center Theater.

The dispute over the character of Atticus was especially charged because of the controversial publication of Ms. Lee’s novel “Go Set a Watchman” in 2015. Some were skeptical that Ms. Lee, who had abandoned the novel in the mid 1950s, was healthy enough to consent to its publication. And many “Mockingbird” fans were shocked by the way Atticus is depicted in “Watchman,” which portrays him as an aging racist and segregationist who opposes his daughter Scout’s more enlightened views on civil rights.

Joseph Crespino, a professor of history at Emory University who recently published a book about Atticus Finch, said that the publication of “Watchman” revealed that Ms. Lee once had a darker view of the character, and turned Atticus into a more nuanced and complex figure.

“The genie is out of the bottle,” he said. “You can’t have the uncomplicated idealistic figure of Atticus, not when we know now that she was struggling to make sense of that character.”