The labor union representing stagehands went on strike Sunday against Atlantic Theater Company in Manhattan, prompting the prestigious nonprofit to postpone two productions that had already begun performances and to warn that union demands could force the closing of the Atlantic and other Off Broadway nonprofits.

Both the International Alliance of Theatrical Stage Employees, the labor union, and the Atlantic said negotiations had broken down, but each side blamed the other for the stalemate. The strike comes at a time when many nonprofit theaters around the country are running deficits and facing serious financial challenges, but also at a time when the labor movement nationally has been emboldened and insistent on better pay and working conditions. Actors’ Equity, the labor union representing stage performers, said it supported the stagehands.

The Atlantic canceled Sunday matinee and evening performances of two new plays, “Grief Camp” and “I’m Assuming You Know David Greenspan,” both of which began previews last week. The Atlantic said Sunday the productions would be postponed indefinitely.

The dispute has broad ramifications for Off Broadway nonprofits, which have for decades nurtured many of the nation’s most acclaimed theater artists and shows. Off Broadway crew members have not traditionally been unionized, but the International Alliance of Theatrical Stage Employees has been working on organizing them, and the Atlantic’s crew voted last February to join the union.

The Atlantic was founded in 1985 and operates two venues in Chelsea. The company has staged more than 200 productions, including three musicals that went on to win the best musical Tony Award after transferring to Broadway: “Spring Awakening,” “The Band’s Visit” and “Kimberly Akimbo.” Another musical first staged at the Atlantic, “Buena Vista Social Club,” is scheduled to begin performances on Broadway next month. The company had an annual budget of $15 million in fiscal 2023, according to a filing with the Internal Revenue Service.

The union, in a statement, accused the Atlantic of stalling negotiations on their first contract and said it had filed unfair labor practice complaints against the company with the National Labor Relations Board, accusing the company of failing to negotiate in good faith.

“Atlantic Theater’s refusal to bargain fairly has left the crew no choice but to strike,” the union’s international president, Matthew D. Loeb, said in the statement. “We are prepared to resume negotiations as soon as Atlantic Theater is ready to bargain in good faith.”

The theater issued its own statement, describing itself as “pro-union” and saying it had made generous offers, but warning that the union’s demands could weaken Off Broadway institutions.

“We have offered a good faith agreement with nearly a 20% increase in wages and other benefits,” the company said.

The company also said, “Most of Off Broadway is facing a precarious financial situation, running significant deficits since returning from Covid. If IATSE is successful in getting their proposed financials with Atlantic, it would set a precedent for other Off Broadway companies and we may see the demise of some of our greatest institutions, including Atlantic.”

The Actors’ Equity assistant executive director, Calandra Hackney, issued a statement of support for the stagehands, saying “Actors’ Equity Association stands in solidarity with these workers,” and adding, “We have full faith that IATSE is negotiating terms that are fair and appropriate for their members, and we look forward to the shows resuming when an agreement has been reached.”