“When the unexpected happens, when the unanticipated happens, we’re just going to work on it,” Mr. Obama said. “We’re going to fix things that aren’t working the way they should be. We’re going to smooth this thing out, and we’re just going to keep on going.’ ”

Lawyers and law enforcement officials said Ms. Sebelius’s decision was unexpected because the insurance exchanges and subsidy payments appeared to fit the definition of federal health care programs in the anti-kickback statute.

Generally, the law makes it a crime to pay or receive anything of value in return for the referral of patients or as an inducement for people to buy goods and services reimbursed by federal health care programs. Such programs are defined broadly as “any plan or program that provides health benefits, whether directly, through insurance, or otherwise, which is funded directly, in whole or in part, by the United States government.”

“The secretary’s decision will have some very significant consequences,” said D. McCarty Thornton, former chief counsel to the inspector general at the Health and Human Services Department. “The federal anti-kickback statute will, in most cases, not apply to subsidized health plans or the items and services furnished by those plans.”

“Plans and providers are very happy to be relieved of that concern,” Mr. Thornton added.

Kevin G. McAnaney, a lawyer who specializes in health care fraud and abuse cases, said Ms. Sebelius’s decision would allow drug companies to give coupons to people who buy insurance through the exchanges.

Such coupons subsidize co-payments and reduce out-of-pocket costs for consumers, encouraging them to use certain brand-name prescription drugs when lower-cost alternatives are available, Mr. McAnaney said.

The federal government has forbidden the use of drug coupons in Medicare and other federal health programs, saying they amount to a classic kickback scheme, with drug companies paying consumers to use their products.