The union president representing workers for a Ronkonkoma-based school bus company said late Sunday night he believes there may still be room to negotiate, just a day after a narrow majority of employees voted to strike.

Timothy Lynch, president of Teamsters Local 1205, said he spoke Sunday night with Glenn Smith, the attorney for Baumann and Sons Inc., and said the bus drivers and other workers will not strike Monday and discussions will continue.

Earlier, Smith warned Lynch that the union had until Wednesday to drop any plans to strike, or the company would pull its final contract offer.

Teamsters Local 1205 workers voted 302-293 Saturday to reject Baumann and Sons Inc.'s proposal and to strike.

Smith said in an email to Lynch earlier Sunday that the process was unfair, adding that Baumann/Acme wouldn't sweeten their final offer.

Lynch said in an email to Newsday that the vote was "absolutely authoritative. . . . There is no doubt that we have been given the authority to strike if and when we deem it appropriate."

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Officials for Baumann and its affiliate Acme contend that not enough workers had the chance to vote -- 595 of about 1,035 eligible union members cast anonymous paper ballots.

In addition, citing the nine-vote margin, Baumann/Acme officials called for the union to hold a new vote this week so all eligible members at company yards may participate.

"Although the union tried to arrange a fair vote, that failed," said Smith in the email to Lynch. "If there is a strike now, the union will be moving forward with an opinion that represents the view of a very small minority of the employees."

Baumann/Acme has extended the final offer, which was set to expire or be accepted at the vote, until Wednesday if there is no strike. After that, the offer is off the table, Smith said.

A strike would affect 15,000 children in Nassau and Suffolk counties who ride the company's buses each school day.

"We have called the union office and the bus company to try to determine whether buses will run tomorrow to no avail," the Commack School District said in a statement issued before Lynch announced buses would run Monday.

Lacking answers, the district -- which relies on Bauman/Acme for all student transportation -- notified parents and staff at 9:30 p.m. Sunday through email, text messages and a robocall, that they did not expect the buses to be running Monday. Less than an hour later, Commack officials had to go through the same means to update everyone that the strike would not start Monday after all.

Lynch refused to say whether the negotiation team would consider a revote, but he defended the process. "Every single member I've spoken to . . . has stated how fair, open and democratic the meeting and vote were," he said in an email to Newsday Sunday.

However, he said in the email, leadership is "engaged in ascertaining the sentiments of the persons who were not present at the meeting."

Now that the union has formally rejected Baumann/Acme's final offer and vowed to strike, many, like Commack school officials, expected an answer on when buses would stop rolling.

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But the vote has not lent clarity to the situation. The last contract ended June 30, and the labor dispute has escalated since late August, when Lynch notified the roughly 35 school districts Baumann/Acme serves that a strike was imminent just as school districts across Long Island were about to resume classes. The company also drives for many of the BOCES centers, special education centers and private and parochial schools to which school districts by law must supply student transit.

Company officials, who have refused to make company president Ronald Baumann available for an interview, said the conflict has cost them $1 million in canceled contracts.

"If there is a strike or any other activity that damages the company's business . . . the LBFO will be immediately withdrawn," Smith said in his email to Lynch.

Mediation ended this month.

The union has sought higher pay, increased contributions for health and other benefits and better working conditions. Lynch said workers want wages and benefits comparable with Baumann/Acme's main competitors on Long Island.

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Officials for Baumann/Acme said the company's final offer would increase its spending on employees by 12 to 14 percent.