Fairfax County supervisors endorsed a $3.2 billion plan yesterday to extend Metrorail to Tysons Corner and Dulles International Airport, giving political and financial momentum to the biggest transit project in the region and one of the largest in the country.

Eight of 11 proposed stations, along a 24-mile extension of the Orange Line between West Falls Church and Route 772, would be built in Fairfax, making the county the largest stakeholder in the project.

Yesterday's 9 to 1 vote, taken after an environmental study and a seven-month public comment period, was one of several government approvals that are required before construction can begin.

Fairfax officials have pledged $500 million for the rail line, and the county's support is key to approval from two panels that will formally vote on the plan late this year, Virginia's Commonwealth Transportation Board and Metro's board of directors. Both panels are expected to seek federal funding next year. Leaders in Loudoun County, where the proposed extension would terminate, endorsed the plan during public hearings during the summer, and the Metropolitan Washington Airports Authority is expected to do the same in the next few weeks.

"This project is vital for this county," said Fairfax Supervisor T. Dana Kauffman (D-Lee), who also serves on Metro's board. "Today's endorsement is a natural response by this governing board to support what people have said they want."

Katherine K. Hanley (D), chairman of the County Board of Supervisors, called the endorsement a "substantial move forward" for a traffic-choked region desperate for ways to get cars off the road.

Only Supervisor Stuart Mendelsohn (R-Dranesville) opposed the project, saying the four stations recommended in Tysons Corner would not serve enough existing office buildings. More development would be required around those stations to justify the rail line, he said. "The next step will be, let's put up high rises around the rail, and you'll have a traffic mess," he said.

Under the proposal, which was recommended by a team of planners from Metro and the Virginia Department of Rail and Public Transportation this month, trains would travel on the median of the Dulles Access Road. A diversion through Tysons would include a short tunnel and underground station in the most congested corner of the huge office and retail park, where nearly half the riders would board or leave the trains. Planners eliminated several options for a bus rapid transit system between West Falls Church and Loudoun, a less expensive system that had been favored by some lawmakers and transportation planners.

The supervisors were dismayed, however, with Virginia's plan to raise tolls as early as next year on the Dulles Toll Road, which parallels the access road. The extra money would cover the state's $800 million share of the cost of the rail project. The board agreed to ask the Commonwealth Transportation Board, which would approve any toll increase, to look for other sources of revenue. Any higher tolls should be set only after construction is underway, they said.

"I don't think there's a problem with our saying that we don't think they should raise tolls, at least until there's some construction in the corridor," said Supervisor Catherine M. Hudgins (D-Hunter Mill), whose district includes a large stretch of the toll road.

The environmental report on the rail project calls for a toll increase from 50 cents to $1 at the main toll plaza. Tolls would rise 25 cents every three years after that until at least 2015.

Pierce Homer, Virginia's deputy transportation secretary, said, "We're looking at all available options for the state's share of the project, and we have made absolutely no decision."

J. Kenneth Klinge of Alexandria, Northern Virginia's representative on the state transportation board, declined to comment on Fairfax leaders' opposition to a toll increase until he saw it in writing. "Today I got the biggest partner that the state has in favor" of the recommendation for a rail-only line, Klinge said.

Virginia plans to seek 51 percent of the capital cost of the rail project, the maximum allowed, from the federal government. Fairfax would pay $514 million, which would be raised partly through bonds and a special tax district for businesses.

About $350 million of Fairfax's share would come from a proposed half-cent sales tax increase for transportation improvements that will appear on the Nov. 5 ballot in Northern Virginia. County supervisors were the first local leaders to publicly support the measure, and yesterday several reiterated their support for it.

"Now all we have to do is get the referendum passed," Hanley said.

"This project is vital for this county," said Supervisor T. Dana Kauffman, who also is a member of Metro's board.Supervisor Stuart Mendelsohn said the Tysons stations would not serve enough existing office buildings.