Medicare, the insurance program for older Americans and disabled people, is run by the federal government. Medicaid, for low-income people of all ages, is financed jointly by the federal government and the states. Eligibility, benefits and provider payment rates vary from state to state.

About seven million low-income people receive financial help through the program for qualified Medicare beneficiaries. Under this program, state Medicaid agencies help pay Medicare premiums, deductibles, co-payments and coinsurance. But states do not have to pay doctors the full amount of such costs, and in some cases they pay nothing, leaving doctors with hundreds or thousands of dollars in unreimbursed expenses.

“Because of this gap in payment, many doctors and other health care providers try to bill the beneficiaries or refuse to provide services to them,” said Denny W. Chan, a lawyer at Justice in Aging, a nonprofit legal advocacy organization.

Many states have adopted policies that limit how much they will pay. For example, a doctor performs a service for a Medicare patient and bills Medicare for $100. Medicare pays 80 percent, or $80, and the doctor could ordinarily collect the other $20 from the patient. But if the patient is also on Medicaid, and if Medicaid’s payment rate for the service is only $70, then the state does not have to make any additional payment, and the claim is considered to be paid in full. The doctor is forbidden to bill the patient for the balance.

Medicaid is supposed to operate like a supplementary insurance policy, filling gaps in Medicare for people who could not easily afford to pay their share of the bills. But under a 1997 federal law, states have the option of making payments based on Medicaid rates rather than on Medicare rates, which saves them money. Medicaid payment rates for physician services are often well below Medicare’s — a reason that some doctors cite for refusing to participate in Medicaid or for limiting the number of Medicaid patients they will see.

The Obama administration has warned doctors that if they participate in Medicare, they “must abide by the balance-billing prohibitions,” regardless of whether they also accept Medicaid patients. “Medicare providers who violate these billing prohibitions are violating their Medicare provider agreement and may be subject to sanctions,” the administration said in a bulletin for doctors.

For their part, doctors say they do not always know that a patient is a qualified Medicare beneficiary and is therefore exempt from Medicare’s cost-sharing requirements. The government is increasing efforts to educate doctors and patients after finding widespread confusion. Federal officials have also reminded private Medicare Advantage plans that they too are bound by the billing restrictions in federal law.