States that have refused a federal offer to expand Medicaid are still seeing significant sign-ups for the safety-net program that serves the poor, and Georgia leads the nation.

In a report released Tuesday that raises political and budget implications, the market analysis firm Avalere Health estimated that at least 550,300 more people had signed up for Medicaid through the end of March in 17 out of 26 states that have not yet expanded eligibility for the program under President Barack Obama’s health care overhaul.

Georgia topped the list, with 98,800 new Medicaid beneficiaries. North Carolina followed, with 58,000. In percentage terms, Montana saw the largest increase: just over 10 percent.

The actual number of sign-ups could be even higher because Avalere did not report data for populous Florida.

Health officials call the surge in sign-ups the “woodwork effect”: People showed up “out of the woodwork” to claim benefits, presumably because publicity about the Affordable Care Act — and fines for failure to obtain health insurance — prompted them for the first time to seek the coverage to which they were already entitled.

However, it’s not clear exactly how many of these beneficiaries are brand new to Medicaid and part of the woodwork effect that states anticipated as part of the Affordable Care Act’s rollout. The latest federal report Avalere used for its analysis notes that “multiple factors contribute to the change in enrollment” seen since last year.

State Medicaid programs frequently experience fluctuations in enrollment. For instance, people who get jobs may fall off the rolls only to rejoin Medicaid later if they get laid off.

The catch for the states that have not expanded Medicaid, the state-federal health care program for the poor, is that they could be getting billions of dollars more from the federal government. Instead, the federal contribution for their additional beneficiaries is determined under a less-generous funding formula than the one for states that accepted the expansion.

“I don’t think a lot of these states anticipated the kind of enrollment they would be getting,” said Avalere CEO Dan Mendelson. “The states are going to have to figure out a way to pay for the increase.”

Virginia, where Medicaid expansion has led to a political impasse between new Democratic Gov. Terry McAuliffe and GOP lawmakers, had nearly 37,000 new beneficiaries, a 3.6 percent increase.

But Texas, the state with the largest proportion of uninsured residents, saw hardly any increase.

The health care law, as passed in 2010, provided for the expansion of Medicaid eligibility to people making up to 138 percent of the federal poverty level — about $16,100 for an individual. The goal was to provide coverage for low-income adults with no children living at home.

But the Supreme Court in a 2012 ruling gave states the right to opt out of that expansion. About half have done so, although some are reconsidering.

The law calls for Washington to pay the full cost of the Medicaid expansion through 2016, gradually phasing down to 90 percent. The federal government contributes a much lower share for the rest of the program, averaging about 60 percent.

Advocates for the poor say states that have not expanded eligibility are already likely to be paying some of the cost of care for low-income, uninsured adults. On top that, they will now have to dedicate more resources to cover additional Medicaid beneficiaries.

“Unlike the states that have expanded, they aren’t seeing any of the benefits of the full federal funding for the newly eligible residents,” said Judy Solomon of the Center on Budget and Policy Priorities.