The play seems likely to have multiple other productions as theaters look for ways to comment on Donald J. Trump’s presidency. Most recently, the Adobe Rose Theater in Santa Fe., N.M., became the fifth theater to commit to presenting it, and Mr. Schenkkan is working on putting together a touring production and considering requests for productions in Canada, Britain and other countries.

The theaters presenting the play say they believe that drama can help shape public understanding and conversation, in this case about an administration whose policies they find troubling.

“History will judge us by how we responded to this crisis, and we can’t waste any time,” said Michael Dove, producing artistic director of the Forum Theater. “We can’t choose silence.”

There is a long history of playwrights using their work to express political concerns in real time. “The Crucible,” Arthur Miller’s 1953 response to McCarthyism, is an oft-mentioned example. More recently, “Stuff Happens,” a play by David Hare about the buildup to the 2003 Iraq War, reached the London stage in 2004; and “Privacy,” James Graham’s response to the 2013 Edward J. Snowden revelations, reached the London stage in 2014. Last year, Berkeley Repertory Theater staged a new adaptation of Sinclair Lewis’s “It Can’t Happen Here,” citing parallels between the book’s plot and Mr. Trump’s candidacy.

The theater world has responded to Mr. Trump in other ways. The evening before his inauguration, many theater artists and patrons around the country participated in the Ghostlight Project, holding outdoor gatherings to express support for tolerance. On Inauguration Day, many Broadway performers sang at a concert to raise money for civil liberties, women’s health and environmental protection organizations.

Two plays coming to Broadway are sure to spark conversation about the current moment. Next month, Lynn Nottage’s “Sweat,” exploring the struggles of working-class Americans, opens at Studio 54, and in June a stage adaptation of George Orwell’s dystopian novel “1984” opens at the Hudson Theater.

“I think a lot of theater artists have been very shaken, and also awoken, by the events in November, and are asking, ‘Am I creating work that’s addressing the questions we all should be asking each other?’ and ‘Am I communicating with as many of my fellow Americans as I can?’” said Ari Edelson, artistic director of the Exchange, which supported the development of Mr. Schenkkan’s play. “It’s very early days for an entirely different constellation of theatrical endeavors than we have seen in the last few years.”