MIAMI — The taxpayer-funded Medicare program paid more than $120 million from 2009 to 2011 in violation of federal law for medical services for inmates and illegal immigrants, according to two reports issued Thursday by federal health officials.

Under federal law, Medicare generally does not pay for services for either group of patients. But the program was billed for more than $33 million in inmate care and more than $91 million for illegal immigrant care over that period, according to the reports from the Department of Health and Human Services inspector general.

In 2011, Medicare expenditures were $549 billion, making Thursday’s figures a fraction of the program’s annual budget. But the reports come as the Obama administration and Congress look for savings in a lean budget year. Putting a dent in Medicare fraud, estimated at $60 billion a year, has the potential for major savings.

The reports recommend that federal health officials establish a better system to automatically flag charges for inmates and illegal immigrants to stop illegal payments before they are made.

The Centers for Medicare and Medicaid Services already had a system in place to do so, but the reports found that the system didn’t catch improper bills until they had already been paid. The reports also noted that the agency didn’t instruct its contractors to try to recoup the lost funds.

The agency agreed in the report that the system needs to be improved, and in April, Medicare is launching a process to help detect and recoup lost money.

“For cases where Medicare is informed of patients’ unlawful presence after claims have been paid, we are working to implement a process for quickly and completely recouping these improper payments,” the agency said in a statement Thursday.

Sen. Tom Carper, D-Del., chairman of the Senate subcommittee on Federal Financial Management, said the improper payments must be recovered, and he commended the agency for its plan to take action.

“Paying more than $120 million in Medicare funds for health care services for people who are clearly not eligible for Medicare benefits is unacceptable,” he said.

The Centers for Medicare and Medicaid Services has already been using a new, highly touted $77 million technology system since 2011 designed to stop fraudulent payments before they are paid.

But lawmakers have been skeptical about the effectiveness of the system, and federal health officials have said they are still working out kinks. Still, initial reports in December showed that the system has saved about $115 million and spurred more than 500 investigations, according to federal health officials.