Most safe abortions are carried out using vacuum aspiration
Restricting the availability of legal abortion does not appear to reduce the number of women trying to end unwanted pregnancies, a major report suggests.
The Guttmacher Institute's survey found abortion occurs at roughly equal rates in regions where it is legal and regions where it is highly restricted.
It did note that improved access to contraception had cut the overall abortion rate over the last decade.
But unsafe abortions, primarily illegal, have remained almost static.
The survey of 197 countries carried out by the Guttmacher Institute - a pro-choice reproductive think tank - found there were 41.6m abortions in 2003, compared with 45.5 in 1995 - a drop which occurred despite population increases.
Nineteen countries had liberalised their abortion laws over the 10 years studied, compared with tighter restrictions in just three.
But despite the general trend towards liberalisation, some 40% of the world's women live amid tight restrictions.
On some continents this is particularly pronounced: well over 90% of women in South America and Africa live in areas with strict abortion laws, proportions which have barely shifted in a decade.
Researchers also noted that while liberalisation was a key element in improving women's access to safer terminations, it was far from the only factor.
Even in countries where abortion is legal, lack of availability and cost may prove major obstacles. In India for example, where terminations are legally allowed for a variety of reasons, some 6m take place outside the health service.
The costs of unsafe abortions, which can include inserting pouches containing arsenic to back street surgery, can be high: the healthcare bill to deal with conditions from sepsis to organ failure can be four times what it costs to provide family planning services.
COUNTRIES WHERE ABORTION HAS BEEN RESTRICTED
1997: Poland re-instated law outlawing abortion except when mother's life at risk or she had been raped
1998: El Salvador outlaws all abortions even when mother's life at risk
2006: Nicaragua similarly eliminates all grounds for legal abortion
Every year, an estimated 70,000 women die as a result of unsafe abortions - leaving nearly a quarter of a million children without a mother - and 5m develop complications.
In the developed world, legal restrictions did not stop abortion but just meant it was "exported", with Irish women for instance simply travelling to other parts of Europe, according to Guttmacher's director, Dr Sharon Camp. In the developing world, it meant lives were put at risk.
"Too many women are maimed or killed each year because they lack legal abortion access," she said.
"The gains we've seen are modest in relation to what we can achieve. Investing in family planning is essential - far too many women lack access to contraception, putting them at risk."
Western Europe is held up as an example of what access to contraceptive services can achieve, and the Netherlands - with just 10 abortions per 1,000 women compared to the world's 29 per 1,000 - is held up as the gold standard.
Here, young people report using two forms of contraception as standard.
Even the UK, which has a relatively high rate, fares well in comparison to the US, where the number of abortions is among the highest in the developed world. The institute says this rate is in part explained by inconsistencies in insurance coverage of contraceptive supplies.
In much of eastern Europe, where abortion was treated as a form of birth control, abortion rates have dropped by 50% in the past decade as contraceptives have become more widely available.
And globally, the number of married women of childbearing age with access to contraception has increased from 54% in 1990 to 63% in 2003, with gains also seen among single, sexually active women.
But there were still significant unmet contraception needs, and a lack of interest among pharmaceutical companies in developing new forms of birth control that provide top protection on demand, the institute said.
Josephine Quintavalle of the anti-abortion Comment on Reproductive Ethics said stopping women falling pregnant in the first place was an area where minds could meet.
"Abortion - back street or front street - is not the answer. Ensuring women have the means to end their pregnancies is not liberating them - they should be able to make real choices before they fall pregnant in the first place," she said.
"But that shouldn't necessarily mean taking pills every day. There will always be problems with access and cost, particularly in countries where people struggle just to buy food.
"What we need is to better understand our fertility - if there are just 24 fertile hours in a month, we need to work out a cheap, effective way for women to know when they can fall pregnant. That would be freedom, and that's what we should aim for."