The number of abortions in the United States has declined in the last 30 years, the report said, but medication abortions, which involve the use of prescription drugs rather than a surgical procedure, have increased and may now account for one-third of abortions.

Representative Diana DeGette, Democrat of Colorado, who requested the investigation, expressed dismay at the findings.

“States are supposed to be covering a limited number of abortions under Medicaid, but are not even doing that,” Ms. DeGette said. “A poor woman who has been raped or raped by a relative or whose life might be endangered by carrying a pregnancy cannot afford to go to another state to get these services. That’s why we have Medicaid covering services like this.”

South Dakota told the Government Accountability Office that it does not cover abortions in cases of rape or incest. Federal health officials sent a letter to South Dakota in 1994 observing that its Medicaid coverage did not comply with federal law.

The federal Centers for Medicare and Medicaid Services is aware that South Dakota “does not cover abortions in cases of rape or incest, as required by federal law, but has not taken any action in 25 years to ensure the state’s compliance,” the report said.

“As a result,” it said, “Medicaid beneficiaries in South Dakota do not have Medicaid coverage for abortions in cases of rape or incest.”

The findings lead to a paradoxical conclusion: The Trump administration, which is firmly opposed to abortion, may now have to work with states to make sure they provide Medicaid coverage for the surgical procedure and for the abortion pill in certain circumstances.