Virginia is withholding millions of dollars needed to run rail and bus systems in the region unless jurisdictions agree to give the commonwealth seats on local transit boards.

The Virginia Department of Rail and Public Transportation gives $168 million each year to the Northern Virginia Transportation Commission. The money helps fund Metro — which receives $93 million — Virginia Railway Express, and bus systems in Arlington, Fairfax and Loudoun counties and Alexandria. Since the fiscal year began July 1, the department has withheld $20 million.

“If this isn’t resolved, it will mean jurisdictions won’t have money to pay their bills,’’ said Jeffrey C. McKay, an alternate member of Metro’s board and a member of the Fairfax County Board of Supervisors. “They’ll either have to stop services they’re providing or they’re going to have to find another source of funding.”

Local jurisdictions and transit agencies, including NVTC, were asked to sign a revised annual contract with Virginia that would allow the state to have a seat on some of their boards. Metro board members from Virginia say they think the state is trying to secure two seats on their board — a voting member, already approved this year by the General Assembly, and an alternate, nonvoting member.

But Thelma D. Drake, director of the Department of Rail and Public Transportation, denied that the state is seeking a second seat on the Metro board through the contract change. She said the agreement would give the state seats on other local transit boards, and she plans to send a letter this week to the Metro board to clarify that.

Drake said she has been trying to talk to the NVTC about the contract since spring, but officials there have not been clear about what their opposition has been.

She said she has spoken three times to Richard Taube, executive director of the NVTC, about the contract.

“I don’t know why this isn’t resolved,’’ Drake said. “It’s unfortunate that we’re at this point. We can’t fix the problem we didn’t know was here.”

However, Kala Quintana, NVTC’s director of communications, said Taube has exchanged at least a half-dozen phone calls and e-mails with the Department of Rail and Transportation, Drake and others on releasing the funds.

Quintana said the agency has lawyers reviewing the memorandum.

“We’re trying to work through any legal concerns we have,” Quintana said. “We’re asking they release the funds until we determine whether we can legally sign the document. We want to keep the region moving and make sure we can pay our bills on time and make sure we can keep buses and transit actually running.”

Virginia Secretary of Transportation Sean T. Connaughton said any locality or agency that signs the contract will receive its money. “If they don’t sign the contract, they won’t receive funds,’’ he said.

Of the 54 entities across the state asked to sign amended transit contracts, only the NVTC, Fairfax, Arlington and Alexandria have refused, state officials say.

The NVTC is expected to meet Thursday in executive session to discuss the contract. Taube is scheduled to talk to state officials Friday.

Virginia Gov. Robert F. McDonnell (R) has long been trying to secure two seats on the 16-member Metro board, saying Metro needs more oversight from state government.

After several failed attempts, McDonnell unexpectedly persuaded the General Assembly to give him the power to appoint a voting member to the Metro board. NVTC elects Virginia’s four representatives on the Metro board.

The governor appointedlawyer James Dyke to the Metro board this month. The change will force the NVTC, composed of 19 local and state elected of­ficials plus the state’s public trans­portation di­rector, to re­linquish one of its seats on the Metro board. Some of the 19 members are from Loudoun, Fairfax and Arlington counties and the cities of Falls Church, Alexandria and Fairfax.

NVTC officials said the NVTC must elect Dyke to the Metro board on Oct. 6, but state officials said the law indicates he should be an automatic member.

“We’re going to follow what the laws says,’’ McDonnell said in an interview. “Now long-term, there needs to be some restructuring of Metro. I think in the short run, all we’re looking at is the localities are going to have to get together and decide who gives up the seat to make room for Mr. Dyke.”

Connaughton said state officials are working on getting a second seat through a change in the agreement that governs Metro, which must be approved by Virginia, Maryland and the District. Congress has to approve a change, and the president must sign it.

But some transit entities and local politicians said they worry that the contract Virginia wants them to sign is a violation of rules for local transit agencies, including Metro.

“Every time Richmond does these kinds of things they call into question whether they are committed to making sure transit works up here,” said Mary Hynes, a voting member of Metro’s board and vice chairwoman of the Arlington County Board. “They keep going around this, holding money back, threatening not to do matches. This is not the way to behave if you want to be a responsible partner.”

Last summer, McDonnell threatened to not pay Virginia’s contribution to a $3 billion federal funding plan for Metro’s capital needs unless the state received two of Northern Virginia’s four seats on the agency’s board.

The federal government agreed to give Metro $1.5 billion for capital needs over 10 years but required that Virginia, Maryland and the District match the money. Virginia eventually paid its $50 million annual contribution. The amended contract does not affect that agreement, Drake said.

“I have no problem with the governor having additional seats,” said Alexandria Mayor William Euille, an alternate Metro board member. “It is a process issue. I don’t think we should be forced into something that has not gone through the proper process and procedures.”

Drake said she does not know which board — if any — the state would try to install a member on because it would be done case-by-case if an issue arose or if the state thought its expertise was necessary.

“If services stop, [the public] will have to look at NVTC and say, ‘What’s the issue?’ ” she said. “They’ve made a decision not to work with us.”