A portion of the Silver Line’s Wiehle-Reston East Station is seen during a tour on Nov. 4, 2013, in Fairfax County. (Matt McClain/The Washington Post)

The head of the Silver Line project said Wednesday that most of the software problems that delayed completion of the $5.6 billion rail line for several weeks have been resolved, clearing the way for contractors to schedule a trial run of the new service next weekend. But officials still have no date for when passenger service will begin.

“Most of the [software issues] are behind us or are on the verge of being behind us,” said Pat Nowakowski, executive director of the rail project. “They are not considered an issue for doing this test.”

The update was welcome news for members of the Metropolitan Washington Airports Authority board, which is overseeing construction of the rail line — one of the largest public works project in the United States — and has faced questions about its stewardship of the project.

Authority officials had hoped to complete the first phase of the project in September, but a series of delays has forced them to revise their timetables.

In December, after authority officials announced the second delay in six months, Sen. Mark R. Warner (D-Va.) sent a letter to the authority questioning whether MWAA and its contractors were doing enough to complete the rail line.

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Officials now say they believe the first phase of the Silver Line will be completed — and ready to be turned over to the Washington Metropolitan Area Transit Authority — next month.

As part of the next set of tests, officials will run 10 eight-car trains along the rail line at the same time Metro is running regular Orange Line service. Testing is scheduled to take place in the evening hours of Jan. 25. Silver Line trains will run between the Wiehle Avenue station and East Falls Church. The testing is expected to be completed by Sunday morning. One of the goals of the test is to see how well the new rail line integrates with the larger Metro system.

While officials have said repeatedly they will not compromise safety in the rush to open the line, they acknowledged Wednesday that the public may be getting impatient for Silver Line service to begin. “Nobody more than us would like to say that we’re there,” said MWAA president and chief executive Jack Potter.

In July, officials said they would need an additional eight weeks to complete work on the multi­billion-dollar project. In addition to safety testing, several of the stations were not yet complete.

Then in November, Nowakow­ski announced further delays after routine testing uncovered problems with the software linked to the line’s automatic train control system — a key safety component that controls train movement and speed and ensures proper spacing between trains traveling along the system’s more than 200 miles of track.

It was the failure of this system to detect the presence of a train on the tracks that was blamed in part for the 2009 Red Line crash that killed nine people and injured dozens of others.

Even after MWAA hands the rail line over to WMATA, it could be an additional 90 days before Metro completes the testing and training needed for Silver Line service to begin. The Federal Transit Administration also must sign off on the project once Metro has finished its testing. While MWAA was responsible for managing construction of the project, Metro is responsible for operating the rail line.

The testing and construction delays aren’t expected to add to the overall price of the project, but they may prove costly to Metro. For each month passenger service is delayed, WMATA stands to lose $2 million to $3 million in fare revenue, officials said.

The first phase of the Silver Line will include five stops, four in Tysons Corner and one at Wiehle Avenue in Reston. Preliminary work on the second phase has begun, and construction is expected to begin this spring. The second phase will have six stops, including one at Washington Dulles International Airport.

Northern Virginia officials see the Silver Line as vital to the economic growth of the region, saying it will attract business and jobs to the region and offer commuters an attractive new option. Fairfax officials, in particular, are hoping the four stops in Tysons Corner will enable them to transform the ­traffic-clogged job center into a bustling, transit-friendly urban center.

But not everyone is thrilled about the new rail line. Many Dulles Toll Road users are indignant that they are paying almost half the cost to build the rail extension. Fairfax and Loudoun counties will pay just more than 20 percent of the costs with additional money coming from the state of Virginia, the federal government and the airports authority.