Only 118 of those doctors, he said, have successfully made it to residency.

“If I had to even think about going through residency now, I’d shoot myself,” said Dr. Fernández-Peña, who came to the United States from Mexico in 1985 and chose not even to try treating patients once he learned what the licensing process requires. Today, in addition to running the Welcome Back Initiative, he is an associate professor of health education at San Francisco State.

The counterargument for making it easier for foreign physicians to practice in the United States — aside from concerns about quality controls — is that doing so will draw more physicians from poor countries. These places often have paid for their doctors’ medical training with public funds, on the assumption that those doctors will stay.

“We need to wean ourselves from our extraordinary dependence on importing doctors from the developing world,” said Fitzhugh Mullan, a professor of medicine and health policy at George Washington University in Washington. “We can’t tell other countries to nail their doctors’ feet to the ground at home. People will want to move and they should be able to. But we have created a huge, wide, open market by undertraining here, and the developing world responds.”

About one in 10 doctors trained in India have left that country, he found in a 2005 study, and the figure is close to one in three for Ghana. (Many of those moved to Europe or other developed nations other than the United States.)

No one knows exactly how many immigrant doctors are in the United States and not practicing, but some other data points provide a clue. Each year the Educational Commission for Foreign Medical Graduates, a private nonprofit, clears about 8,000 immigrant doctors (not including the American citizens who go to medical school abroad) to apply for the national residency match system. Normally about 3,000 of them successfully match to a residency slot, mostly filling less desired residencies in community hospitals, unpopular locations and in less lucrative specialties like primary care.

Over the last five years, an average of 42.1 percent of foreign-trained immigrant physicians who applied for residencies through the national match system succeeded. That compares with an average match rate of 93.9 percent for seniors at America’s mainstream medical schools.