On Sunday, hours after talks broke down, the cash-strapped company canceled Monday rehearsals for a Feb. 12 opening production of Verdi’s “La Traviata” in Brooklyn.

“This is a very sad day for what once was a spectacular cultural icon and for the people who performed its music,” said Alan Gordon, national executive director of the American Guild of Musical Artists representing the chorus, stage directors and principal singers.

Local 802 of the American Federation of Musicians represents the orchestra. Both unions have been without a contract since the spring.

Gail Kruvand, chairwoman of the orchestra union’s negotiating committee and its assistant principal bass player, said union members “made a good-faith effort to say that, yes, we are willing to sacrifice for the sake of ensuring that the grand tradition of the City Opera lives on.”

But she said the company’s rejection of union proposals could be “the death knell for one of New York’s cultural treasures.”

City Opera is now operating on a shoestring, offering orchestra and chorus members minimum fees for an already abbreviated season. City Opera moved out of its longtime home at the Lincoln Center for the Performing Arts last year, citing financial troubles, and cut back its usual schedule of 12 to 16 operas per season, with a peak of about 130 performances.

In a statement, the company said it had “no choice but to lock out” union members because they rejected the company’s economic offer and had threatened to strike when performances began, according to a statement released Sunday. Both labor unions have passed strike-authorization votes.

City Opera General Manager George Steel said his company couldn’t enter rehearsals with a musician strike looming for performances scheduled in February at the Brooklyn Academy of Music, one of the various venues around New York booked for 16 shows of four productions.

However, “we have no intention of hiring replacement workers,” company spokeswoman Risa Heller said. She didn’t know whether that meant the season wouldn’t open next month.

The opera and the unions have been in talks with Allison Beck, deputy director of the Federal Mediation and Conciliation Service, since mid-December. Those negotiations broke down Saturday night.

The musicians rejected the company’s offer, saying the financially diminished company doesn’t guarantee work or pay. Steel said the company, facing “economic constraints,” can only afford to pay people “for the work that they do.”f

Under a contract management proposed in early December, the musicians’ average annual income would drop from about $40,000 to as little as $5,000 for two productions. For decades, musicians were guaranteed at least 22 weeks’ work.

City Opera’s troubles started about a decade ago with multimillion-dollar deficits, followed by the appointment of Belgian director Gerard Mortier as general manager and artistic director, effective as of the 2009-2010 season. Accustomed to staging expensive, cutting-edge extravaganzas in Europe, he insisted that City Opera’s theater be renovated, forcing the company to go dark for the 2008-2009 season, with only six unstaged performances elsewhere.

The economy’s free-fall was a last straw for the 69-year-old company that former New York Mayor Fiorello LaGuardia dubbed “the people’s opera.”

Income from ticket sales during the dark season plunged to about $186,000, down from $12 million. And the company raided its endowment to the tune of tens of millions of dollars.

Mortier resigned from his position about six months before he was officially to start, on grounds that the operating budget had dwindled.

“We’re heartbroken, but we cannot save the company,” said Kruvand, the bass player.

She said City Opera has been “unable to sell tickets or attract donors” — mostly because Steel abandoned the company’s longtime practice of staging surefire operas along with pioneering new works. Recently, the company has presented mostly 20th-century operas that are a box office challenge.

Kruvand noted that the current general manager still makes more than $300,000 after a 10 percent pay cut, while the musicians face about a 90 percent cut in earnings.

“We don’t feel George Steel is capable of running an opera company,” said Kruvand, adding that when the star soprano Sills became general manager in the 1980s, she led a company “that was a platform for nurturing careers.”

Speaking for Steel, Heller said that the unions “have repeatedly vilified George.”

But the negotiating process is “not about any one person,” she said. “This is about whether the unions will finally recognize that the City Opera needs to make fundamental changes in the way it operates so that it only pays people for work they perform.”

Gordon, the union leader, called the latest labor impasse “City Opera’s death.”