Read more about this story from CNN affiliate WPRI.

(CNN) -- Termination notices have been sent to every teacher in the Providence public school system, setting off a wave of anxiety and anger in the Rhode Island city and prompting a union leader to accuse the mayor of anti-union maneuvering.

The teachers will remain at work as the school year continues, though the notices sent out this week mean any of them now could lose their jobs at municipal officials' discretion. During a packed and at-times spirited meeting Thursday night, the city school committee voted 4-3 to back Mayor Angel Taveras' move to send out the notices.

The mayor said in an online message Wednesday that he authorized the previous day's decision to dismiss almost 2,000 teachers and staff to allow for greater flexibility as the budget process unfolds. Taveras said officials will later determine the final number of layoffs -- as well as exactly which teachers in which schools might lose their jobs -- needed to balance a multimillion-dollar budget gap.

"It gives us more flexibility to recall teachers based on student need," said Christina O'Reilly, a spokeswoman for the district.

That explanation did little to assuage teachers in the firing line, nor did a closed-door forum Thursday with Superintendent Tom Brady on the matter.

"The mood in the meeting today was extremely grim," teacher Lori Iannucci told CNN affiliate WPRI. "Teachers felt very negative, unappreciated. No questions were answered."

Teachers said that their union wasn't notified beforehand of the termination notices. At Thursday's meeting, they said they were given general assurances that the situation could be resolved within the next month.

Taveras insisted that he values Providence's "gifted teachers" and only felt compelled to act given a March 1 deadline to notify municipal employees about "potential changes to their employment status."

But Steve Smith, president of the city's teacher's union, said he believed the decision "makes no sense at all to teachers or the community." He accused Taveras of "making a political decision to take control and silence workers" -- a group that, he said, has consistently and continually worked with city leaders to implement reforms.

"It's shocking that in the midst of working in a collaborative environment ... the mayor says you're fired," Smith told reporters. "This sounds very much like what's going on in Wisconsin, Ohio and Indiana, where lawmakers want to get rid of collective bargaining and remove the voice of workers."

In a statement, American Federation of Teachers President Randi Weingarten called the decision "stunning," especially given that the union and city "have been working collaboratively on a groundbreaking, nationally recognized school transformation model."

"We looked up 'flexibility' in the dictionary, and it does not mean destabilizing education for all students in Providence or taking away workers' voice or rights," said Weingarten, whose organization includes 1.5 million teachers and staff. "Mass firings, whether in one school or an entire district, are not fiscally or educationally sound."

This isn't the first time a Rhode Island community has gained headlines with a mass firing. Last year, all teachers were fired at Central Falls High School, a square-mile city just north of Providence. This issue was over low-student performance, though a deal later was reached to hire many of them back.

Insisting that "spending reductions are inevitable," Taveras cites budgetary problems as the reason for the moves, not performance. At a conference last week, Smith said that U.S. Secretary of Education Arne Duncan singled out Providence twice for educational reform efforts, such as its teachers union being among the first to sign up for the Race to the Top initiative.

Taveras said he was "hopeful we can work together to address the fiscal challenges we face." Teachers, though, said they were left with worries about how they'd continue the school year and survive beyond that.

"How do we motivate our students to continue to value (us) as educators when our power has been taken away from us?" said Iannucci. "We'll do our best. Really, what can we do?"