The nonprofit theatre said it recognized that its contemporary staging of the play, which portrays Caesar as a magnetic, blond businessman with a gold bathtub, had provoked heated debate. Actors and other artists threatened on Monday to boycott the two companies that ended their sponsorship.
"Such discussion is exactly the goal of our civically-engaged theatre," it said in a statement.
"Our production of Julius Caesar in no way advocates violence towards anyone. Shakespeare's play, and our production, make the opposite point: those who attempt to defend democracy by undemocratic means pay a terrible price and destroy the very thing they are fighting to save," the theatre said.
Before Monday night's performance, which received a standing ovation, the play's director, Oskar Eustis, delivered a statement, which he urged audience members to record on their cellphones.
"Neither Shakespeare nor The Public Theater could possibly advocate violence as a solution to political problems and certainly not assassination," he said.
Theatre lovers were quick to point out that a national tour of Julius Caesar in 2012 by The Acting Company featured a Caesar played by a black actor in a modern business suit who had a resemblance to then-president Barack Obama, a Democrat.
Sponsors of the Guthrie Theater, including Delta, apparently had no objections when that show landed in Minneapolis.
Presidents portrayed as Julius Caesar in U.S. productions: Lincoln, Reagan, Clinton, GWB, Obama, Trump. (Caesar died in all of them.)— @bubbaprog
Sponsors react after Trump Jr. post
Delta and Bank of America ended their support of the production on Sunday, hours after Trump's son Donald Jr. questioned in a tweet whether it was art or political speech.
"Disappointed in @Delta for turning its back on free expression. I've flown many thousands of miles with you. No more," tweeted Beau Willimon, an American playwright and creator of the popular Netflix series House of Cards.
Actor Ron Perlman, known for his big-screen depiction of Hellboy, also condemned the two former sponsors. "Act accordingly," Perlman told his followers on Twitter.
Other defenders included Scott M. Stringer, the New York City comptroller, who wrote letters to the heads of Delta and Bank of America, arguing that dropping their support "sends the wrong message."
He writes: "Art matters. The First Amendment matters. Expression matters." He enclosed copies of the play with the letters.
"I hope you enjoy it — it is a classic, in any age," he wrote.
'Crossed the line'
"Had this intention been made known to us, we would have decided not to sponsor it," the bank's statement said.
The two companies also received support on social media.
"Kudos to @Delta for pulling $$ from 'play' portraying assassination of @POTUS," former Arkansas Governor Mike Huckabee, a Republican whose daughter is deputy White House press secretary, wrote on Twitter. "No one should sponsor crap like that!"
The National Endowment for the Arts said in a statement that while it had given the New York Shakespeare Festival $320,000 US over the past four years, no NEA funds were awarded to support the Public Theater's production of Julius Caesar.
American Express Co, which calls itself "the official card of The Public Theater," said on Monday it did not support this version of Julius Caesar, but did not say if it would drop funding.
"The Public Theater puts on many shows. Our sponsorship does not go toward the funding of the production of Shakespeare in the Park and we do not condone this interpretation of the play," American Express said in a statement.
Comedian Kathy Griffin faced a backlash in recent weeks after posing for a photograph with a fake severed and bloodied head resembling Trump. After images were published on social media, Griffin lost sponsorships and jobs, including co-host of CNN's New Year's Eve coverage.
Long known for provocative, challenging works
The Public has long been an incubator of provocative and challenging works, unafraid to mount plays that comment on current events or update Shakespearian plays to explore modern themes.
'Any sense that this political regime is imposing a kind of censorship and the free market can help correct it will probably be good for the Public [Theater]' - Laurence Maslon, New York University Tisch School of the Arts
Laurence Maslon, an administrator and arts professor at New York University's Tisch School of the Arts, said it was disingenuous for large corporations that have backed the Public for years and enjoyed co-opting its downtown cool vibe to sound alarmed now.
Maslon said he thinks any loss of funding the Public experiences from corporate defectors will be compensated for by donations from liberal grass-roots groups and people worried about the apparent threat to artistic freedom.
"I can imagine any sense that this political regime is imposing a kind of censorship and the free market can help correct it will probably be good for the Public," he said.
Julius Caesar ends its run Sunday. The comedy A Midsummer Night's Dream begins in the park on July 11.