WASHINGTON — States have been granted additional time to establish markets through which millions of Americans are expected to buy subsidized private health insurance.

Under the law, the federal government was supposed to determine “on or before January 1, 2013,” whether states were prepared to operate the online markets, known as insurance exchanges.

But Health and Human Services (HHS) Secretary Kathleen Sebelius, working with the White House, said she would waive or extend the deadline for any states that expressed interest in creating their own exchanges or regulating insurance sold through a federal exchange.

Administration officials said they are trying to persuade states to share the work of running an exchange, supervising health plans and assisting ­consumers.

Every state is supposed to have an exchange by October, and most Americans will be required to have health care coverage starting in January 2014. The federal government will run the exchange in any state that is unwilling or unable to do so.

Last month HHS announced $1.5 billion in new “Exchange Establishment Grants” to California, Delaware, Iowa, Kentucky, Massachusetts, Michigan, Minnesota, New York, North Carolina, Oregon and Vermont.

“These states are working to implement the health care law, and we continue to support them as they build new affordable insurance marketplaces,” Sebelius said.

In another key area of health care, HHS released a report in January that asserts that Medicare’s costs are rising at historically low rates at the same time that senior citizens are receiving more benefits.

HHS said Medicare’s spending for each senior rose 0.4 percentage points last year, the third straight year with low cost ­increases.

Both the Medicare actuaries and the Congressional Budget Office have also projected that low cost increases will continue for several years — to a major extent because of the new health care law’s cuts in payments to insurance companies and providers.