The company’s statement came after reports that a Rockette was “embarrassed and disappointed” that the decision to perform had been made for her. The dancer’s private Instagram post was published by the gossip website Perez Hilton and aggregated by other outlets.
That dancer, Phoebe Pearl, did not immediately respond to multiple requests for comment on Friday, nor did several of her fellow performers.
The company’s statement seemed to contradict an email from the American Guild of Variety Artists to some of the dancers, which was forwarded to The New York Times.
“If you are full time, you are obligated,” that message read. “Doing the best performance to reflect an American institution which has been here for over 90 years is your job. I hope this pulls into focus the bottom line on this work.”
Heather Lang, a contemporary dancer who left the Rockettes in 2009 after five years with the company, said in a phone interview that there were about 12 full-time dancers within the company who perform in both winter and spring shows.
Ms. Lang, 35, said that performers were drawn to the company for the honor to dance at Radio City Music Hall and for the health benefits, but that many of the women have feared standing up for themselves in the current controversy without support from the union.
‘“One of the most annoying situations about that job is, it’s corporate,” Ms. Lang said. “It’s not like a Broadway show where you feel like you have an artistic voice. You’re sort of owned by this corporation.”
She added: “Everybody’s in fear of losing their job.”
The American Guild of Variety Artists did not immediately respond to a request for comment. Nor did Eric Greene, a lawyer for the guild. The Madison Square Garden Company did not respond to further questions about whether or not full-time Rockettes were required to perform at the inauguration.
The idea that Rockettes could be forced to perform prompted anger among actors, performers and other celebrities on Twitter, who began widely circulating contact information for the company, the Rockettes producers and their union.
Chris Pappas, a tour guide with Radio City Music Hall, said employees at Madison Square Garden were angry about the prospect of Rockettes being forced to perform.
“I can say that as a member of the tour guide staff, we have discussed it, and it has upset us,” Mr. Pappas said in a telephone interview. “It’s not saying the Rockettes are invited to perform. It’s saying that the Rockettes will perform.”
On Thursday, James L. Dolan, the executive chairman of the Madison Square Garden Company, said in a statement that the Rockettes were “treasured American icons,” and noted that they had performed at the inaugurations of George W. Bush in 2001 and 2005.
The dance company, known for pearly smiles and high kicks, is one of the most recognizable holiday institutions of the president-elect’s hometown, and one of the few performers to confirm an appearance so far. The Mormon Tabernacle Choir, which has performed at previous presidential inaugurations, confirmed its appearance on Thursday. On Friday, a petition was circulating among people who were urging the group to reconsider.
Last week, Boris Epshteyn, a spokesman for Mr. Trump’s inaugural committee, confirmed in an email that the 16-year-old opera singer Jackie Evancho would be performing the national anthem at the event, calling her a “true role model and inspiration for people young and old in our country and around the globe.”
Other performers, including the Italian tenor Andrea Bocelli and the singer Elton John, have both said in recent days that, contrary to rumors, they would not be performing.
In between commenting on Twitter about the proliferation of nuclear weapons and addressing business conflicts of interest within his family, the president-elect took time on Thursday evening to assure the nation that he did not want A-list celebrities attending his inauguration.
“I want the PEOPLE!” Mr. Trump tweeted.
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