The U.S. Postal Service, which negotiated a contract with its biggest labor union that would save $3.8 billion over 41 / 2 years, will not save enough under that agreement, the agency’s top House overseers said Tuesday.

The contract with the American Postal Workers Union will not return the agency to profitability, said Rep. Darrell Issa (R-Calif.), who is chairman of the House Oversight and Government Reform Committee.

“This contract falls short,” Issa said at a hearing about the Postal Service’s labor costs. “We have deep concerns that some of the provisions of the contract may in fact be the wrong direction, to less flexibility, less ability to trim the workforce and less ability to, in the future, make the kinds of investments we need to make.”

The Postal Service, which has reported losses for five consecutive quarters, said Monday that the contract would not reduce labor costs to less than the current 80 percent of total costs. The Postal Service has said it will run out of cash unless Congress permits it to delay a $5.5 billion payment, due Sept. 30, for health benefits for future retirees. The labor costs include payments for those benefits.

“While it is the nature of negotiations that neither side got everything they wanted, I will tell you this is the best possible outcome we could have achieved given the legal framework in which we operate,” Postmaster General Patrick R. Donahoe told the panel. “This is a responsible agreement.”

The agreement, which must be ratified by the American Postal Workers Union members, would apply to the labor group’s 202,000 employees and would freeze wages for the first two years of the 41 / 2-year contract.