Health insurers in the marketplaces created by the Affordable Care Act will be reimbursed this year only 13 percent of the money they are owed under a program designed to help cushion the burden of covering large numbers of people who need expensive medical treatment.

Federal health officials said Thursday that insurers owed money through the three-year program are entitled to nearly $2.9 billion for coverage they provided in 2014. The government will pay them $362 million.

A senior official with the Centers for Medicare and Medicaid Services said the agency would pay whatever it can next year and the year after. But the official, briefing reporters on the condition of anonymity, acknowledged that the ability to fully pay hinges on Congress’s willingness to provide additional money.

The program, creating what is known as “risk corridors,” is one of three subtle but significant strategies built into the 2010 health-care law to try to deter insurers participating in the new marketplaces from mainly seeking out customers who are healthy and thus use little medical care. In different ways, all three methods essentially shuttle money from insurance carriers with light medical bills to those with heavy bills.

The risk corridors program is one of two designed for the health exchanges’ initial years. It is supposed to help insurers with costs that are substantially greater than they expected. Originally, the program was not required to pay for itself, but, in a 2015 funding bill, congressional Republicans forbid the Health and Human Services department to use any of its other resources for the program.

Another wrinkle surfaced in August, when CMS said that its first look at the information submitted by insurers found many data errors, so the payments would be delayed. The announcement Thursday came after about half of the insurers in the exchanges were required to correct that prior information.

The senior CMS official said the underpayments may create “some isolated solvency and liquidity challenges” but declined to elaborate on where those may arise. Health industry analysts have said the lack of full payments are most likely to harm new insurers that have been trying to gain a toehold in the exchanges.

The industry’s main trade group, America’s Health Insurance Plans, reiterated its opposition to the constraints Congress has placed on the program’s funding.

“Stable, affordable coverage for consumers depends on adequate funding of the risk corridor program,” said Marilyn B. Tavenner, the group’s president. “It’s essential that Congress and CMS act to ensure the program works as designed and consumers are protected.”