More than half the deaths, about 38,000, are in sub-Saharan Africa, which was singled out as the region with by far the lowest rates of contraceptive use and the highest rates of unintended pregnancies.
The report was compiled by the New York-based Guttmacher Institute, which supports abortion rights and is a leading source of data on abortion-related trends.
"In almost all developed countries, abortion is safe and legal," said Sharon Camp, the institute's president. "But in much of the developing world, abortion remains highly restricted, and unsafe abortion is common."
The report calls for further easing of developing nations' abortion laws, a move criticized by Deirdre McQuade, a policy director with the U.S. Conference of Catholic Bishops' Secretariat for Pro-Life Activities.
"We need to be much more creative in assisting women with supportive services so they don't need to resort to the unnatural act of abortion," McQuade said.
The institute estimated the number of abortions worldwide fell from 45.5 million in 1995 to 41.6 million in 2003, the latest year for which global data was available.
A key reason for that drop, the report said, was that the portion of married women using contraception increased from 54 percent in 1990 to 63 percent in 2003.
The report recommends expanding access to modern contraceptives and family planning services; expanding access to legal abortion services; and improving post-abortion care services.