The president of the American Medical Association yesterday told President Reagan that voluntary work by the nation's doctors is doing a better job of providing health care to unemployed persons who are without medical coverage than any new government program.

The Reagan administration is debating whether to provide government-funded health care for the estimated 10.7 million Americans--workers and their families--who have lost medical benefits as a result of losing their jobs.

Members of the Senate Finance Committee have been pressing the administration for a commitment to a plan, and are scheduled to discuss a government health care plan for the unemployed in committee on Thursday.

However, after a meeting yesterday between the president and health care groups involved in the administration's private sector initiatives, the president of the AMA said the problem of providing health care for the unemployed is being met by private physicans.

"It's a great problem and we're meeting it . . . , " said Dr. William Y. Rial, president of the AMA. "Our voluntary efforts will be more effective if it continues to grow than any federal program."

Doctors in more than 40 cities have started giving thousands of hours of free or low-cost medical care to the unemployed in formal programs, an AMA official said.

In addition, "what must be thousands" of doctors are "just on their own and without any publicity" caring for as many as a fifth of their patients without payment, said Dr. John Coury, a Port Huron, Mich., surgeon who is vice chairman of the AMA board of trustees.

Northern Virginia doctors said 250 Arlington County physicians--the Arlington County Medical Society's entire membership--are starting a program to give free medical, laboratory and hospital care to patients with no source of payment. Fairfax County doctors have agreed to care for such patients for $1 or $2 a visit.

"We recognize that the federal government has to have an increased part, no question about it," Coury said, but "we also think it has to be a joint effort between industry and government and the physicians."

Some authorities think 20 million persons may be without health insurance or Medicare or Medicaid coverage or any other health plan.

David A. Stockman, director of the Office and Management and Budget, has argued that voluntary efforts by doctors, local governments and private companies should be used to aid the jobless because any federal program would be costly.