A labor dispute between a private school bus firm and its workers over pay, working conditions and benefits remains unresolved, leaving open the possibility of a strike for about 35 districts in Nassau and Suffolk.

The conflict is between Ronkonkoma-based Baumann and Sons Buses Inc. and Teamsters Local 1205. If the union strikes, it could affect 15,000 students. The contract expired June 30.

Union president Timothy Lynch issued a statement Sunday saying officials will set a "firm" deadline this week by which a deal must be reached, but he did not elaborate. Otherwise, workers will strike, he said.

The union has asked Baumann and its affiliate, Acme Buses, for raises, better benefits and working conditions.

The company argues it's made extensive concessions, including pay increases, and the union has been inflexible in demands for raises of 16 percent to 34 percent.

Union leaders announced Sept. 20 that they had unanimously rejected the firm's 90-page final offer, would schedule a vote for their members and asked Baumann to return to negotiations.

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But no vote has taken place, and Baumann officials issued a statement a few days later, on Friday, saying the company had provided the union a summary of its position -- not a final deal.

After learning of union plans for a vote, the company sought and received a list of the union's unresolved issues.

"Local 1205 is simply asking for more, even though parties have bargained for over 100 hours . . . and despite the fact that many compromises have been made," the statement read.

The company said it's agreed to "substantial" wage increases, greater company health contributions and other concessions.

Mechanics and maintenance workers would have pay increases all three years.

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Lynch said the company is far from meeting union pay demands. About 400 employees -- including drivers' assistants -- make between $11.10 and $13.80 per hour, he said. Drivers make $17.20 to $22.90 hourly.

"It would be in extreme bad faith for a strike to be called by the union at this juncture," Glenn Smith, the Newark attorney representing Baumann, said in a statement issued Sunday.

He said mediation was never formally closed and the mediator won't be available until Oct. 7.

Lynch said the union will not agree to more than a dozen of the elements of the company's current proposal, including lack of hourly first-year pay increases for most workers.