Officials for a Ronkonkoma-based school bus company announced Thursday night that they couldn't reach an agreement with the workers' union on its "final offer" and will no longer negotiate.

The dispute between Baumann & Sons Buses Inc. and Teamsters Local 1205 could affect about 35 school districts in Nassau and Suffolk counties that the company contracts with.

"A strike is exceedingly likely," union president Timothy Lynch said in an email. "The company's position on a number of key issues is simply unacceptable."

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The union has been threatening to strike since late August, calling for Baumann and its affiliate, Acme, to provide higher pay, better benefits and improved working conditions.

The union's membership is scheduled to vote on the proposal Oct. 17.

The company, which transports 15,000 students every school day, made a three-year contract proposal Thursday that officials said increases overall employee spending by 12 percent to 14 percent.

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Baumann has requested that a federal mediator be present at the union meeting "to ensure a fair presentation of the package being offered," and to oversee the vote and the tally of ballots.

The strike threat had school districts and parents across Long Island scrambling to prepare backup plans for student transportation just as school was starting in September.