The decisions by the two companies came after days of criticism online and in right-leaning media outlets that was amplified by Donald Trump Jr., a son of the president, who appeared to call into question the theater’s funding sources on Twitter on Sunday morning. By the end of the day, both corporations had distanced themselves from the production.
“No matter what your political stance may be, the graphic staging of ‘Julius Caesar’ at this summer’s Free Shakespeare in the Park does not reflect Delta Air Lines’ values,” the company said in a statement on Sunday night.
“Their artistic and creative direction crossed the line on the standards of good taste,” the company said. “We have notified them of our decision to end our sponsorship as the official airline of the Public Theater effective immediately.”
Bank of America followed hours later, saying it would withdraw financial support from the production of “Julius Caesar” but would not end its financial relationship with the theater, which a spokeswoman, Susan Atran, said had lasted for 11 years.
“The Public Theater chose to present ‘Julius Caesar’ in a way that was intended to provoke and offend,” Ms. Atran said. “Had this intention been made known to us, we would have decided not to sponsor it. We are withdrawing our funding for this production.”
The play is scheduled to open Monday at the Delacorte Theater in Central Park as part of the Public Theater’s free annual Shakespeare in the Park festival. It has been in previews since May 23.
The theater, its financial supporters and its production of “Julius Caesar” have recently faced a wave of criticism online and in right-leaning media outlets.
Last week, Breitbart, the far-right website formerly run by the White House adviser Stephen K. Bannon, compared the play to the controversial online photo that showed the comedian Kathy Griffin holding a severed head that resembled the president. (Ms. Griffin was fired as co-host of CNN’s New Year’s Eve program over the incident.)
But the play’s treatment of Caesar’s grisly assassination has also been questioned by theater critics, including Jesse Green of The New York Times. In his review, he wrote that the depiction of a Trump-like Caesar’s “bare, wound-ripped flesh” — something not called for in the original text — may make viewers wonder, “Has it gone too far?”
Criticism of the play reached a fever pitch on Sunday when Fox News reported that it “appears to depict President Trump being brutally stabbed to death by women and minorities.” Donald Trump Jr., a son of President Trump, joined in shortly after that report, seeming to question the theater’s funding sources.
The play nods frequently to Mr. Trump and 21st-century America. Caesar is portrayed as a tempestuous blond man in a blue suit with a svelte Slavic wife often by his side. The set design includes a blowup of the preamble to the United States Constitution. Some of the costumes are accented by Anonymous masks and the pussy hats favored by some Trump protesters.
Candi Adams, a spokeswoman for the Public, declined to comment on Sunday night on the uproar. She said the director of the play, Oskar Eustis, the theater’s artistic director, would be busy on Sunday evening with the Tony Awards.
Other corporate sponsors of the Public Theater, which include American Express and The Times, have also faced calls on social media to denounce the play or end their relationship with the Public.
Representatives for those companies did not respond to emails seeking comment on Sunday night, but none had publicly announced any change in their relationship with the theater.
Last month, Gregg Henry, who stars in the play as the Trump-like Julius Caesar, told the website Backstage that he believed the comparison was apt because the Roman ruler “became drunk with ego, drunk with power, drunk with ambition and the belief that he and he alone must rule the world.”
Mr. Henry added, “Hopefully, I’m able to sort of show what’s happening with this president, tweak this president for kind of what he is in a lot of ways and also show the dangers of dealing with a tyrant or possible tyrant in our country.”
But in a director’s note published online, Mr. Eustis makes clear that the play does not endorse the assassination of Julius Caesar or any other political leader in a democracy, even if the assassins believe themselves to be acting for the good of the country.
“Julius Caesar can be read as a warning parable to those who try to fight for democracy by undemocratic means,” Mr. Eustis wrote. “To fight the tyrant does not mean imitating him.”