Metro’s board of directors voted unanimously Thursday not to appeal a federal judge’s ruling that members of the union representing most of the transit agency’s employees be given a pay increase.

Amalgamated Transit Union Local 689, which has about 10,000 members, had been in arbitration with Metro over a 9 percent wage increase for its members to be awarded in 3 percent increments in 2009, 2010 and 2011.

The dispute began in 2008 after the union and management reached an impasse on contract negotiations; the issue went to arbitration. In 2009, the arbitration board ruled in favor of the union on some issues, but the transit agency appealed the decision.

The case went before U.S. District Judge Peter J. Messitte, who in a ruling last month concurred with the arbitration panel. Metro’s board could have appealed Messitte’s decision but decided against doing so after an hour-long, closed-door executive session Thursday.

“We strongly disagree and were dismayed to learn the court’s perspective that wage increases are easily absorbed by our riders and stakeholders, a view we do not share,” Chair Catherine Hudgins said in a statement. “These increases are not sustainable by our customers or our funding jurisdictions.”

Jackie Jeter, president of Local 689, said she was “happy they decided not to appeal naturally, but I wasn’t so thrilled about the statements they put out.” She said the board’s statements made it “sound as if the wage increase was going to do some significant harm to the riding public.”

Jeter said she thinks the judge “did look at whether the wage increases would have been absorbed by the stakeholder, and he made a determination that for public transportation, what we were asking for is not unreasonable.”

The Metro board said it did not want to prolong the three-year legal dispute, which has cost the agency $1.5 million in legal fees.

“We want to put this matter behind us so that our employees can remain focused on serving our customers, but clearly we regard an award of this magnitude as generous given the extraordinary economic constraints under which our customers and our taxpayers are living,” said Hudgins, who is also a member of the Fairfax County Board of Supervisors. “Many people in the region have received less, including zero increase in wages, furloughs and pay cuts.”

Jeff C. McKay, an alternate, non-voting board member who also is a Fairfax supervisor, called the judge’s decision “very unfortunate.”

“This economy is not the time for big retroactive pay increases,” McKay said in an e-mail. “I think the court missed a chance to practice good common sense.”

McKay said he “very reluctantly” went along with the board’s decision not to appeal the judge’s ruling. “We basically did not feel like continued court challenges would end in our favor.”

Metro officials said that the money had been set aside in the agency’s operating budgets for the payout and that this year’s budget will not be adversely impacted. Officials said the wage increases will cost the agency $96 million, plus $8 million in pension contributions.

Tom Bulger, an alternate, non-voting board member representing the District, said the wage increases the union won were “unsustainable.”

“Unless you have money from the tooth fairy, you can’t keep asking the jurisdictions to kick in money and raising fares,” he said.

Non-voting and voting members of the board reached a consensus in a closed session, and the board’s principal members voted in an open session that followed.

Metro General Manager Richard Sarles told employees of the board’s decision in an internal e-mail. He said the agency’s human resources and finance departments would come up with a “plan for distributing the retroactive wage increases.” Metro officials said details of when and how employees would be paid would be released in coming weeks.

Hudgins said given the union’s success, she does not see “any basis for budgeting a general wage increase” when the union contract comes up next year.

“We need to build the organization up, and you don’t do that by fighting each other,” Hudgins said. “We have to work on safety, reliability and rebuilding the system. This is a distraction.”