Loudoun County officials are exploring what would happen if they withdrew funding for the Metrorail extension to Dulles International Airport.

The Board of Supervisors on Tuesday directed county staff to determine how Dulles Airport’s operations and the rail extension would be affected.

A decision by the Metropolitan Washington Airports Authority last month to build an underground Metro station at Dulles has drawn widespread criticism from federal, state and local officials concerned about the rising cost of the second phase of the project. Critics favor an aboveground location that would save $330 million.

The airports authority “is causing this project to derail,” said Scott K. York (I), chairman of the Board of Supervisors. “The numbers aren’t adding up, and when the numbers don’t add up, you can’t continue making decisions that are costing the project more and more.”

The 23-mile Metrorail extension to Route 772 in Loudoun is being built in two phases. Loudoun’s share of the estimated $3.5 billion second leg would rise to $300 million, officials said, based on an underground location for the Dulles stop.

Airports authority board member Mame Reiley, who chairs the Dulles rail committee, said she was hopeful that Loudoun would stay on with the project, which, she added, “will bring incredible economic development to Loudoun.”

The first phase, connecting to the existing system near East Falls Church and extending to Wiehle Avenue in Reston, is scheduled to open in 2013 with five stations and will cost $2.75 billion.

The second phase is expected to have six stations, including the one at Dulles, and could open by 2016.

Fairfax County has committed to financing 16.1 percent of the rail project’s total cost; Loudoun is expected to pay 4.8 percent; and the airports authority would finance 4.1 percent. The rest of the project would be paid for with state and federal funds and with revenues from the Dulles Toll Road.

Meanwhile, the nonprofit Washington Airports Task Force on Tuesday recommended trimming up to $780 million from the cost of the second phase.

Leo Schefer, president of the Dulles-based group, called funding of the project “the most serious crisis” since the White House’s decision to close Reagan National Airport for several weeks after the Sept. 11, 2001, attacks.

“The focus tends to be on the station being above- and below ground. I don’t think that’s the issue,” Schefer said.

The task force, which is funded by both public grants and the private sector to support aviation services, suggested that the airports authority work with Loudoun and Fairfax to negotiate third-party agreements for parking garages at Metro stations along the extension. As an example, Schefer noted Fairfax’s public-private deal to build a parking garage and bus facilities at Reston’s Wiehle Avenue station, which is the last stop on the rail project’s first phase. The deal is part of a planned residential and office complex near the station.

A similar strategy at the six Metro stops along the second leg would save the rail project $100 million to $200 million, the task force said.

The group recommended building an initial, scaled-back rail yard at the airport to save $50 million to $100 million and proposed that an interest-free state loan or grant would reduce project costs by $100 million to $150 million.

Reiley said the airports authority board has been considering the cost reductions recommended by the task force.

“We are in agreement on almost all of his points, as they were things that the committee has asked the staff to look into over the last year,” Reiley said.

The task force warned that additional borrowing from the bond market to fund the rail extension could jeopardize the airports authority’s ability to enhance passenger service and expand Dulles Airport. One such project is a planned concourse that would bring passengers closer to the AeroTrain that opened last year.