Metro is worried it could lose more than $180 million a year in penalties if a new labor contract is so costly that the transit system can’t keep its budget under a cap imposed by Maryland and Virginia in the landmark funding agreement.

A three-member arbitration panel began a critical phase Monday in closed-door proceedings on a contract to set pay and benefits for Amalgamated Transit Union Local 689, Metro’s largest union.

The union is seeking a three-year contract, with a 4 percent wage increase in each year, according to people familiar with both sides’ positions, who spoke on the condition that they not be named to describe confidential talks. The union also is seeking additional adjustments for holiday pay, night work and cost-of-living allowances.

Metro is proposing a four-year contract that includes a three-year wage freeze. Workers would get a 2 percent pay increase in the fourth year, with the possibility of an additional 1 percent raise if ridership recovers.

The two sides also have a major disagreement about pensions for future hires.

Management says that unless the arbitrators ultimately rule in its favor on all significant elements of the contract, Metro would be forced to consider dramatic service cuts or seek larger operating subsidies from the jurisdictions that support it.

The subsidy requests would exceed a 3 percent cap on annual increases in such contributions, according to people familiar with the agency’s position.

That would automatically force Virginia and Maryland to cut some subsidies to Metro by 35 percent under legislation recently passed by each state’s legislature. Virginia Gov. Ralph Northam (D) and Maryland Gov. Larry Hogan (R) have said they will sign the bills.

The cuts represent about $54 million in Virginia and $132 million in Maryland for the fiscal year that begins July 1, and they would be a significantfinancial setback for Metro at a time when it is celebrating a historic regional accord to increase its funding by $500 million a year.

“It would torpedo the current budget,” said an individual who described management’s position. “As a practical matter, Metro would have to cut service radically.”

The outcome of the contract talks will have a large impact on Metro’s costs because labor accounts for about 70 percent of its total operating expenses. No money for potential wage increases was included in the agency’s budget for the coming fiscal year.

A Metro spokeswoman declined to comment. A union spokesman reaffirmed previous criticisms of the 3 percent ceiling, which was included in the Virginia and Maryland bills as a way to pressure Metro to restrain its spending in exchange for giving it increased funding. The District has not imposed a cap.

“Local 689 finds the 3 percent number to be arbitrary, and we are concerned about it,” spokesman David Stephen said. “However, it is premature to determine an outcome before the process is over, before the arbitration panel has even considered this.”

He added that the union “will continue to respect the process of not litigating the arbitration hearing through the media.”

ATU Local 689, which represents 8,400 active Metro workers and 3,500 retirees, has been working under an expired contract since July 2016. Its contract typically sets the pattern for pacts with Metro’s other four unions, which are much smaller.

Average pay for Metro workers covered by the union is about $70,000 a year, the agency said.

The union and management entered arbitration when contract talks deadlocked in September. Both sides have now presented their cases to the arbitrators. The rebuttal phase, in which each party challenges the other’s arguments, began Monday and is scheduled to end Thursday.

The panel is expected to issue its decision in late spring or early summer. Either side could then challenge the decision in court.

Wages and pensions are the most significant areas of disagreement. Management wants to save money by providing a less generous pension system for future hires. Current employees would continue to have a defined benefits plan, but new employees would have a defined contributions plan, similar to a 401(k).

On health care, management wants changes in co-payments and pharmacy benefits.

The union wants no changes to pension or health benefits.

Management has complained in the past that the arbitration process favors the union. That’s because the union can always argue that Metro can afford to pay more, such as by raising fares, cutting service or asking the jurisdictions that support it to increase their subsidies.

Metro General Manager Paul J. Wiedefeld proposed a year ago to amend a federal law known as the Wolf Act to strengthen management’s hand in arbitration cases. The proposal is included in a bill introduced in December by Rep. Barbara Comstock (R-Va.).

The bill has not had a hearing in the House. An alternative bill, backed by Democratic House members from the Washington suburbs, does not include the proposed change.

Under the arbitration process, management and the union each select one member of the panel. In practice, this often means the third member casts the decisive vote.

Metro selected Jonathan C. Fritts, a partner with Morgan, Lewis and Bockius. ATU Local 689 selected Thomas R. Roth, president of the Labor Bureau, a consulting firm.

The neutral member is Richard I. Bloch, a nationally known arbitrator who has worked in cases involving professional sports, airlines and the steel industry. (The Washington Post has profiled him for his work on the side as a magician.)

None of the three arbitrators would comment, but there was general agreement that Bloch is the one to watch.

“The good news is everybody respects him, but I wouldn’t want to be Rich right now — he’s really in the hot seat,” said an individual active in the proceedings.