The first phase of the new Metrorail line to Dulles Airport could run as much as $150 million over budget, the head of the construction project said Wednesday.

Executive Director Pat Nowakowski told the Metropolitan Washington Airports Authority board during a meeting that the project is going to come in “very close” to its projected price tag of $2.8 billion. The 11 1 / 2 miles of rail will run from Falls Church through Tysons Corner to Reston.

“We have some work to do to try to bring that in,” Nowakowski said. “We have a lot of challenges.”

Among the issues, he said, is whether Metro will pay for some of the changes it wants, including a safety system that alerts train operators when a worker is on the tracks. The move complies with recommendations made by the National Transportation Safety Board, officials said. The NTSB recommendations came after two incidents in 2006 in which Metro workers were killed while on the tracks.

The airports authority is overseeing construction and is scheduled to turn the line’s operation and maintenance over to Metro in the summer 0f 2013.

“Anytime you make changes after a contract has been awarded, you wind up paying more money,” Nowakowski said.

The $150 million estimate is the scenario if “some of the worst fears come through,” he said after the meeting.

Cost overruns could be recouped from “different places,” Nowakowski said, including through “reducing the project’s scope.” He declined to elaborate because he said he wanted to review the issues with the project partners, including the counties, the state of Virginia and Metro.

Dan Stessel, Metro’s chief spokesman, said the transit agency has “not received any formal request” from the airports authority about sharing costs. Metro has to “ensure that the Dulles extension is built to the same safety and reliability standards as the rest of the Metrorail system,” he said.

Metro “has and will continue to work with MWAA to manage project costs,” Stessel said, “including approval of numerous cost-saving measures that do not compromise safety or reliability.”

Airports officials have said Metro’s changes have amounted to $49.3 million, already taken out of a contingency fund.

Bill Cobey, an MWAA board member, said after the meeting that he had “a lot of confidence” in the airports authority staff’s ability to “accomplish the mitigation.”

“I’m not so naive to think they can accurately predict the outcome,” he said. “I’d just like it to come close” to the estimated cost, he added.

The first phase of the project began construction in 2009 with a $312.2 million contingency fund. About $82 million is left, Nowakowski said. The project, which is more than half complete, has $1.3 millionremaining in its regular budget, he said.

Nowakowski added that any cost overruns would be paid for based on a funding formula in which the local jurisdictions and the airports authority contribute set percentages of the cost that total 25 percent. But officials have said that the percentage of the cost born by Dulles Toll Road revenue also rises as the cost rises.

Federal, state and local officials are still debating how to pay for the $2.8 billion second phase of the Silver Line and to contain its costs. Plans call for that segment to run from Reston to Dulles International Airport and Loudoun County.

On Wednesday, board members also discussed potential sources of revenue for that leg. There is a push to have Virginia contribute $150 million and to receive some federal loans. The Department of Transportation committed a $900 million grant for the first phase but has made no commitment for the second.

Tom Davis, the former Virginia congressman and an airports authority board member, suggested having the airport access road’s users pay a toll. But Charles Snelling, the chairman of the board, said that could harm Dulles.

Jack Potter, chief executive of the airports authority, said there is a “whole host of legal issues” in tolling users of the airport road because it is a federally owned property.