Stakeholders involved in planning the Metro system’s rail line to Dulles International Airport and Loudoun County said Tuesday that they are closer to an agreement on how to build and finance the second phase of the multibillion-dollar project.

The working group of about a dozen representatives from the Metropolitan Washington Airports Authority, Metro, Fairfax and Loudoun counties, and the Virginia Department of Transportation met with U.S. Transportation Secretary Ray LaHood at his headquarters for an hour to discuss details of the second phase of the rail line that will stretch from Reston Town Center to Dulles Airport and Ashburn.

Representatives declined to discuss specifics about the meeting. They would say only that progress had been made.

In July, LaHood and stakeholders agreed upon a framework for development. The deal was designed to trim hundreds of millions of dollars from the $3.5 billion cost of the second phase.

For LaHood’s compromise to work, it will take support and money from the local, state and federal investors. Loudoun and Fairfax counties have agreed in principle to help pay for a rail station and parking garages to support the project. At this point, the group is hammering out details of the agreement.

The counties and the airports authority want federal funds, and the project is looking for the state of Virginia to put up money for the rail line. The project cleared a major hump when the airports authority reversed course this summer and supported a less expensive aboveground station for Dulles after months of debate.

LaHood has scheduled another meeting with those involved for Sept. 23.

The Dulles rail line will include 23 miles of additional track with 11 stations. It is being built in two phases. The first part, which runs from East Falls Church to Wiehle Avenue on the eastern edge of Reston, is under construction and is expected to be completed in 2013. The second phase will serve Reston Town Center, Dulles Airport and Ashburn.