A Metrorail station at Dulles International Airport will be built underground, giving hurried travelers sheltered access near the airport terminal.

But convenience will come at a price.

The station will cost about $330 million more than an aboveground stop, according to a report by the Metropolitan Washington Airports Authority, which is managing construction of the 23-mile extension of Metrorail from East Falls Church to Ashburn.

The airports authority’s board approved the more expensive underground station Wednesday, even as it faced criticism from state and local funding partners.

Mame Reiley, who chairs the board’s Dulles rail committee, called the aboveground option a “second-class station [at a] first-class airport.”

The underground stop will be closer to the main terminal, about 550 feet away. The aboveground station, next to the north garage, would have been 1,150 feet away.

“If you’re a family, and you’re traveling to India, and you have a lot of kids and a lot of luggage, that’s a long haul,” Reiley said after the vote.

The board voted, 9 to 4, in support of the underground option. The dissenting votes were cast by former Virginia congressman Thomas M. Davis III, Michael L. O’Reilly, Frank M. Conner III and William W. Cobey Jr.

Davis, who was one of the board’s most outspoken critics of an underground station, said he was concerned about its financial impact on Fairfax and Loudoun counties. Fairfax is funding its portion of the rail project with two special tax districts.

“The financial burden on our end falls to our partners,” he said.

Davis also worried that the cost could lead to additional increases in fees on the Dulles Toll Road, where revenues are supposed to pay for more than 50 percent of the rail line. The airports authority approved a three-year schedule of increases in 2009 but would need to hold public hearings before implementing more.

“For a lot of working people, these tolls are the only viable” way of commuting, he said.

The first phase of the 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. With a Dulles station underground, the second phase is projected to cost $3.5 billion.

Federal, state and local officials criticized the board’s decision, noting the ballooning cost of the second phase, which was originally estimated to be $2.5 billion. The federal government committed $900 million to the first phase but has no funding commitment for the second leg.

Rep. Frank R. Wolf (R-Va.), who had requested an audit of the rail project and of the airports authority, said in a statement that, “I am disappointed and share the concerns of state and the local partners. Everything possible needs to be done to keep costs down on this project.”

In a letter to the airports authority, Virginia Secretary of Transportation Sean T. Connaughton, also expressed concern about the cost.

“The tunnel alignment, by all accounts, is a more expensive alignment than the aerial option through the airport and will place a heavy financial burden on local funding partners and Dulles Toll Road users,” he wrote.

Fairfax officials have endorsed the less-expensive aboveground option.

Sharon Bulova, chairman of the Fairfax Board of Supervisors, said the airports authority should cover the $330 million difference between the aerial and underground stations.

“We’re looking out for our constituents,” she said.

The airports authority board said it would try to find other cost reductions within the rail project, noting that the extra cost of an underground station is about 5 percent of the project’s total price tag.

“To me, that’s a manageable cost,” board member Robert Clarke Brown said.

The underground option will cost $912 million to build and is scheduled to be completed in mid-2017, compared with the aboveground station, which was expected to be finished in late 2016.

Airports officials said the underground option will save up to $330 million compared with an estimate released in September. That estimate had put the second phase’s costs at $3.83 billion and included a planned tunnel and underground station at Dulles airport.

The airport authority’s board then directed staff members to consider alternative locations for a rail stop in an effort to reduce the cost of the second phase. The board debated the merits of four potential sites for the station, before narrowing it down to two choices.

Last month, the board dropped one option for an underground stop leading into the main terminal because of its cost. In January it rejected a proposed outdoor site for the airport station, noting the cost and scope of the project and its potential to ruin views of the terminal, an architecturally significant building designed by Finnish American architect Eero Saarinen.