Federal, state and local officials want the board that manages Dulles International Airport to reconsider its decision to build a new Metrorail station there underground, but board members intend to move ahead with the plan — despite questions about the cost of the choice and who would pay for it.

Mame Reiley, chairwoman of the Dulles rail committee for the Metropolitan Washington Airports Authority, said reopening the issue “would not be in the best interest of the public and the authority we serve.”

“I’m not going to put it on the [committee’s] agenda, and if it was something that came up in the board meeting, I’d vote against it,” she said.

The airports authority board, which is supervising the construction of a 23-mile extension of Metrorail from East Falls Church to Ashburn, voted last week to build the underground station, which will cost an estimated $330 million more than an aboveground stop.

Although money for the project is coming from several sources, there is no appeals process for decisions made by the board. Fairfax and Loudoun officials said their representatives have been shut out of the process.

The airports authority board “has made a decision, as though they could make a decision in isolation of the funding partners that need to be at the table with them,” said Sharon S. Bulova, chairman of the Fairfax County Board of Supervisors.

Rep. Frank R. Wolf (R-Va.), who has requested an audit of the rail project and a review of the authority’s operations, will hold a press conference with Loudoun lawmakers on Monday asking for a reversal of the decision.

Fairfax, Loudoun and Virginia officials have drafted a joint letter to Charles D. Snelling, chairman of the authority board, criticizing the decision, refusing to pay for the additional cost and asking the board to take steps to keep the overall price tag as close to the original “estimate of $2.5 billion as possible.”

“If they still want an underground station, then [the airports authority] should pay for it,” said Virginia Secretary of Transportation Sean T. Connaughton.

Loudoun officials are expected to sign off Monday on the letter, which has already been approved by Fairfax and the state.

Airports authority board members have said they will search for cost savings in other elements of the project, such as a planned rail yard at Dulles and the six Metro stations along the second phase of the line.

“We’re committed to find every single cent possible to reduce the cost of phase 2,” Reiley said.

“There are big project elements in this besides the Dulles station,” added board member Robert Clarke Brown.

Snelling said he has not seen the letter but plans to invite state and county officials for a discussion.

“The board has voted 9 to 4 for the underground alignment. If my partners have a problem with that, I certainly want to sit down with them and talk about how we can resolve that,” Snelling said.

The first phase of the Metro rail extension , which is costing $2.75 billion, connects with the existing rail system near East Falls Church and consists of four stations in Tysons Corner and one at Wiehle Avenue in Reston. It is scheduled to open in 2013.

The second phase would run from Wiehle Avenue to Ashburn in eastern Loudoun and is projected to cost $3.5 billion with an underground Dulles station.

Fairfax 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 a combination of state and federal funds and with revenues from the Dulles Toll Road. Local and state officials have expressed concerns that growing costs will lead to steep increases in tolls.

It is unclear how the dispute could affect the construction timeline for phase 2, which is expected to open in 2017. The authority expects to solicit bids this year, and officials say they are committed to keeping the project on track.

“I take all of the eventualities seriously,” Snelling said. “I’m concerned about doing the project right, I’m concerned that the project could be endangered. I’m concerned about all of those things.”

Bulova said she is looking forward to a resolution.

“I’m hopeful that we will be able to come to some agreement,” she said. “Having rail to Dulles is one of our number one transportation priorities.”