Now that the Transport Workers Union has turned down the Metropolitan Transportation Authority’s contract offer, some observers are saying the pressure will grow on the state to step in and negotiate a settlement to avoid another transit disruption.

The chairman of the MTA, Peter Kalikow, is planning to file an official request for binding arbitration with the New York State Public Employees Relations Board this week, a MTA spokesman said.

If the request is accepted, an arbitration panel made up of members picked by each side will hear presentations from the union and the MTA, and make a final decision. Union members will not vote on the new contract.

On Friday, the TWU announced that its members voted down the tentative contract by a margin of just seven votes. The vote, which was conducted by e-mail and phone, was 11,234 against and 11,227 for the contract. Seven votes represents a fraction of a percentage point of the number of voting transit workers. Nearly a third of the union’s membership didn’t vote.

Union leaders, including the president of TWU Local 100, Roger Toussaint, from the beginning of the dispute have emphatically resisted binding arbitration. A spokesman for the union said it will continue to fight any attempts to stop face-to-face bargaining.

A labor historian at New York University, Daniel Walkowitz, said he expects the two sides to go to arbitration, despite the rhetoric coming from union leaders.

“There’ll be some saber rattling, but they’ll go to arbitration,” he said. “There is a sense that the public won’t tolerate another strike … and the work force is divided enough that they probably won’t vote for another strike.”

Mr. Walkowitz said he expects a new contract won’t look radically different from the one reached on December 20, at the peak of the three-day strike, but that it will likely include “some gesture for the younger workers,” who he said returned to work with substantially smaller victories than older workers.

A former director of labor relations for the city, Robert Linn, said any changes will likely be made within the same “cost structure” created by the first round of contract negotiations.

He said the specifics will have to be hammered out after the transit workers tell the union leadership what stopped them from ratifying the contract.

A vice president on the union’s executive board who has been critical of Mr. Toussaint, John Mooney, said the vote was swayed by Mr. Toussaint’s concession that would have had workers paying 1.5% of their health care premiums.

Mr. Linn said he doubts the city will negotiate over the unprecedented health care concession because it has such high-level political support, including Mayor Bloomberg, who has said other public sector unions should follow suit.

Announcing the results of the vote Friday, Mr. Toussaint blamed a contingent of dissenting union leaders, including vice presidents Ainsley Stewart and Mr. Mooney and an executive board member, Martin Goodman, for swaying some members from accepting a good contract. He also said Governor Pataki’s threats to veto a clause in the preliminary contract that would give workers an additional $130 million for pensions hurt confidence in the contract.

The preliminary contract included wage increases of 3%, 4%, and 3.5% over the next three years. During mediation, MTA officials dropped their demand that the age for full retirement be pushed to 62 from 55, but the union conceded to pay a portion of health care premiums. Transit workers agreed to return to work without knowing the details of the contract agreement. Mr. Mooney said this is a sore point for many of the workers and some union leaders, who feel they were cut out from the final negotiating process.

Mr. Mooney said workers might agree to pay a fixed amount of their health care premiums, but that a percentage based system hurts the transit employees who work the most hours the most.

Labor observers and union members doubt another strike is likely, but said smaller types of work disruptions are possible. With no contract, looming Taylor Law fines in the millions, and the possibility of jail time for Mr. Toussaint and other union leaders, the euphoria that followed the settlement of the labor dispute seems to have subsided. Straphangers, meanwhile, must wait to see how the next round plays out.