The Obama administration told states Monday that they couldn’t do a partial expansion of Medicaid under the health-care law and still receive full federal funding, disappointing many Republican governors on one of the most important questions surrounding the health-care law.

In recent weeks, these governors, along with other state officials, had shown increasing interest in the idea of a partial expansion of the state-federal program for the poor and disabled. In ruling that option out, the administration has raised the stakes for states debating whether to participate in a part of the law that is crucial to its success.

The 2010 law called for states, starting in 2014, to open their Medicaid programs to people with incomes up to 138 percent of the federal poverty level. Under the law, the federal government will pay the entire cost of covering newly eligible individuals for the first three years. After that, the federal government’s share declines, reaching 90 percent by 2020. If all states were to take part in the full expansion, an additional 18 million Americans would be covered by Medicaid.

But many state leaders, especially Republicans, have been leery of sharply expanding their Medicaid programs; many worry that the federal government might reduce funding. As an alternative, they have floated the idea of partial expansions — extending coverage, for instance, to all adults with incomes up to 100 percent of the poverty level — while still having the federal government foot the entire bill.

On Monday, Secretary of Health and Human Services Kathleen Sebelius said no. In a memo to all 50 governors, she said that “the law does not provide for a phased-in or partial expansion.”

States might still be able to get federal dollars to do a partial expansion, the memo said. But at least from 2014 through 2016, those states would receive their regular federal match rate — which varies from 50 percent to 78 percent, depending on the state. States would also have to apply for federal permission for such a partial expansion.

After 2017, the memo said, states might be able to get the higher federal match for a partial expansion as part of a broad “innovation waiver.” States can apply for such waivers starting that year.

These waivers exempt states from many of the law’s specific mandates as long as they can prove that there will be no increase in the numbers of uninsured residents and that insurance plans will be no less affordable or comprehensive.

Interest in the partial expansion idea has been growing since June, when the Supreme Court found that states can’t be penalized for opting out of the law’s full expansion.

In a statement Monday, Louisiana Gov. Bobby Jindal, chairman of the Republican Governors Association, said that by removing the possibility of partial expansion, the administration had made the decision facing states “more difficult.”

“The Obama Administration’s refusal to grant states more flexibility on Medicaid is as disheartening as it is short-sighted,” Jindal said.

There is no deadline by which states must declare their intentions regarding the Medicaid expansion. The decision will rest largely with state legislatures as they wrestle with 2014 budgets in the coming months.

So far, just more than a dozen states appear certain to take part in the expansion. In about 13 states, officials have been leaning heavily against it. In the remaining states, the decisions are still very much in doubt.

Matthew Salo, executive director of the National Association of Medicaid Directors, said it is hard to predict how many states will go along with the expansion now that the choice is all or nothing.

“It pushes some of those states that were pushing for partial expansion to yes and some to no. . . . It will be a mixed bag,” he said.

Douglas J. Holtz-Eakin, a former director of the Congressional Budget Office and a critic of the health-care law, predicted that many state leaders will shy away from expansion because they don’t trust Congress to leave the higher matching rate untouched.

“The fundamental question state leaders have to ask is, ‘Do I believe that I will continue to get 90 percent of the cost of the expansion [covered by the federal government] forever, given that the federal government has no money?’ ” Holtz-Eakin said.

Such concerns were fueled by Obama’s willingness to consider reducing the total federal contribution to Medicaid during his unsuccessful deficit negotiations with House Speaker John A. Boehner (R-Ohio) last year. His proposal would have reduced the federal contribution to Medicaid by tens of billions of dollars over a 10-year period.

Obama scaled back the idea in his proposed 2013 budget, offering to reduce federal spending on Medicaid by less than 1 percent.

In Monday’s memo, the administration said it no longer supports even that more modest idea. “The Supreme Court decision has made the higher matching rates available in the [health-care law] even more important to incentivize states to expand Medicaid coverage,” the memo said.

In a blog post Monday, Sebelius also announced that the administration had approved the plans of six states — Colorado, Connecticut, Maryland, Massachusetts, Oregon and Washington — to run the health insurance marketplaces, or “exchanges,” called for under the law. States wishing to run their exchanges have until Friday to submit their blueprints. The administration will sign off on those plans on a rolling basis.

If a state is deemed unable to operate an exchange, or simply chooses not to, the law empowers the federal government to step in and run it.