In an interview on Tuesday, Mr. Polisi said that while its subject matter is difficult, “I believe it is one of John Adams’s greatest works.”

More recently, when the Opera Theater of St. Louis presented “The Death of Klinghoffer” in 2011, it took the opportunity to have a number of interfaith dialogues before it was performed. Rabbi Howard Kaplansky, the chairman of the Michael and Barbara Newmark Institute for Human Relations at the Jewish Community Relations Council of St. Louis, attended. He said in an interview that Jews and Muslims had discussed the opera, and the issues it raised, and attended together.

“I think it was a constructive experience,” he said.

But the opera, dogged by controversy, has long had its detractors. Its premiere, at the Théâtre Royal de la Monnaie in Brussels in 1991, was moved from January to March when the Belgian interior minister requested that it be delayed until the end of the gulf war. Scheduled performances at the Glyndebourne Festival Opera and the Los Angeles Opera, two of the companies that commissioned “Klinghoffer,” were canceled, and it was not until this March that the work was presented in Southern California, by the Long Beach Opera.

After Lisa and Ilsa Klinghoffer, the daughters of Leon Klinghoffer, saw the opera at the Brooklyn Academy of Music in 1991, they denounced it, releasing a statement saying that it appeared to be anti-Semitic. The Klinghoffers said on Tuesday, in a statement released by the Anti-Defamation League, that they believe the work “perverts the terrorist murder of our father and attempts to romanticize, rationalize, legitimize and explain it.”

Choruses from the opera were supposed to have been performed by the Boston Symphony Orchestra in November 2001, but those concerts were canceled in the aftermath of the Sept. 11 terrorist attacks. (The husband of a chorus member was killed in the attacks.)

In recent days, several Jewish groups expressed concerns about the Met’s plans to mount the opera. Abraham H. Foxman, the national director of the Anti-Defamation League, had several discussions with Mr. Gelb. While he praised the decision to cancel the simulcast, he noted that some groups would still be unhappy that the work was being performed at all.