Fairfax County officials approved a plan Tuesday to build five residential towers near a future Metro rail station in Tysons Corner.

The Board of Supervisors voted unanimously to permit a rezoning request by the McLean-based Georgelas Group. The high-rises, which are the first project to be approved under Fairfax’s new urban building plan for Tysons, will replace a parking lot and a one-story industrial park about a block away from the Metro station.

Despite their support, some supervisors noted they have yet to adopt a financing plan to pay for an estimated $1.7 billion in road and transit upgrades needed in Tysons through 2030. These costs exclude the first phase of the Metrorail extension to Dulles International Airport, which Fairfax is helping to fund through a special tax on landowners.

Supervisor Patrick S. Herrity (R-Springfield) said that unless a financing plan for roads is in place, he would be “hard-pressed” to support other Tysons redevelopment proposals awaiting county approval.

“There’s only so much money in a development project and there is so much money we can ask our taxpayers to pay,” he said.

But Supervisor Jeff C. McKay (D-Lee), said Fairfax’s urban plan for Tysons was originally inspired by the coming of Metro rail.

“It’s a transportation investment that’s driving the entire plan and why we’re here today,” he said.

The Georgelas Group has agreed to try to buy 2.8 acres that could be developed into athletic fields near a wooded park. Providing recreational space is one of several development conditions under Fairfax’s urban plan for Tysons.

Pamela Konde, president of the Greater Tysons Green Civic Association, urged the board to consider the impacts athletic fields could have on her neighborhood of about 350 homes adjacent to Tysons.

“I am not ashamed to say we live in suburbia, not an urban place,” she said.

The Georgelas towers are part of the company’s Spring Hill Station project, about 32 acres of residential, office and retail buildings near a future Metrorail station at Leesburg Pike and Spring Hill Road. The rest of the project could come back before the board late this year.