WASHINGTON — The Supreme Court agreed on Monday to decide whether the federal government was entitled to break a promise to shield insurance companies from some of the risks they took in participating in the exchanges established by President Barack Obama’s health care law, the Affordable Care Act.

In their brief seeking Supreme Court review, two insurance companies said they had been the victims of “a bait-and-switch of staggering dimensions in which the government has paid insurers $12 billion less than what was promised.”

The health care law established so-called risk corridors meant to help insurance companies cope with the risks they took when they decided to participate in the law’s marketplaces without knowing who would sign up for coverage. Under the program, the federal government would limit insurance companies’ gains and losses on insurance sold in the marketplaces from 2014 through 2016.

If premiums exceeded a company’s medical expenses, the insurer would be required to pay some of its profit to the government. But if premiums fell short of medical expenses, the insurer would be entitled to payments from the government.