Washington’s airports authority wants more money from federal and state governments to build the second phase of the Metro rail line to Dulles International Airport.

The board of the Metropolitan Washington Airports Authority, which is overseeing construction of the extension to Dulles and Loudoun County, said Wednesday it wants Virginia to contribute $500 million and the federal government to provide loans of $700 million to $1.2 billion.

“The federal government really needs to step up to the plate,” said Mame Reiley, who chairs the Dulles Corridor Committee for the airports authority’s board. She said Transportation Secretary Ray LaHood has called the Dulles project “one of the most important” transportation projects in the country.

“We’re saying to him: We agree, so show us the money,” she said.

The administration of Virginia Gov. Robert F. McDonnell (R) has not been clear publicly about whether the state plans to contribute $150 million toward the project. McDonnell has objected to the board’s decision to require the lead contractor to sign a work agreement with organized labor.

Virginia Transportation Secretary Sean Connaughton said Wednesday that the state has no plans to contribute $500 million.

“We don’t have it, and we have no intention of giving it,” he said. “Our goal is to get this project back to the original price tag so we can move forward, and the state has already provided the Dulles Toll Road and its revenues to move this project at $2.5 billion.”

Without the additional funds, Reiley said drivers would still have to pay higher rates along the Dulles Toll Road. The revenue is being used to help fund the new rail line. One-way tolls could rise from $2 to $13 in 20 years and to $17 in 30 years, according to an analysis by the airports authority.

With the money, “that’s where the tolls would go down,” she said.

The second part of the Dulles line will run from Reston to Dulles Airport and continue to Loudoun County. It is estimated to cost about $3.5 billion, although federal, state and local officials hope to trim hundreds of millions more from the price.

For months, the region’s local leaders and the airports authority board quarreled about whether to locate the Dulles station above or below ground. Last month, the board voted to approve a deal brokered by LaHood to put the Dulles station above ground, a cost savings of at least $330 million and a reversal of its previous position.

As part of the deal, Loudoun and Fairfax counties are expected to help reduce the overall cost by finding a way to pay for parking garages and the Route 28 station. They are trying to identify public-private partnerships for those deals, and also plan to apply for the same federal money — known as TIFIA, or Transportation Infrastructure Finance and Innovation Act loans — that the authority wants, according to Fairfax County Board of Supervisors Chairman Sharon Bulova.

Bulova said the counties are working with LaHood to determine the costs and their options for paying their portions.

“Fairfax would need TIFIA to make it affordable,” Bulova said. “LaHood was encouraging about TIFIA being made available to the counties, not [the airports authority].”

Details of LaHood’s agreement are being ironed out with officials in Loudoun and Fairfax counties. Some members of the airports authority board expressed concern about whether the localities would meet their end of the deal.

“People were asked to share the sacrifice,” said Robert Brown, a member of the airports authority board. “To give up stuff they wanted, to take on some pain. We gave up the underground station and all the players were asked to do things.

“Now they seem to be saying they’ll use their best efforts to do it but a deal is a deal,” Brown said. “Now everybody has to stick to it.”

The first phase of the Dulles project, which runs from Falls Church through Tysons Corner to Reston and is expected to open in 2014, is on time and on budget, according to Pat Nowakowski, executive director of the Dulles project. He briefed the board at its committee meetings Wednesday.

“We will be very close,” he said of the projected cost for Phase 1, which officials have said is $2.75 billion. The federal government committed $900 million to the first phase.

He said Kawasaki, the manufacturer of the new 7000 series rail cars that will run on the Dulles line, has experienced some work issues after the tsunami in Japan. Metro officials said they are “monitoring the situation” and expect to know closer to the end of the year how it might impact production of the rail cars.