This is certainly not true. As MCCL has pointed out:
The legalization of abortion may not make the procedure less risky, but it does have one clear consequence: legalizing abortion increases the number of abortions. In the United States, the abortion number skyrocketed from an estimated 98,000 per year to a peak of 1.6 million following total legalization in 1973. Explains Stanley Henshaw of the Guttmacher Institute (an advocate for legalized abortion), "In most countries, it is common after abortion is legalized for abortion rates to rise sharply for several years, then stabilize, just as we have seen in the United States."Professor Michael New adds this about the Guttmacher study:
In South Africa, for example, the number of abortions rose from an estimated 1,600 in 1996, the year before abortion was legalized, to 85,621 in 2005. By contrast, when Poland finally prohibited most abortions following decades of government-funded abortion on demand, evidence suggests that the total number of abortions (legal and illegal) fell dramatically.
However, the [conclusion that pro-life legislation is ineffective] is faulty. Most of the countries where abortion is prohibited are in Africa, the Middle East, and Latin America. These countries have low per capita income and a higher incidence of social pathologies that may increase the perceived need for abortion. This nuance is not picked up in any of the media coverage of the AGI [Guttmacher] report.
Interestingly, AGI has also released research that demonstrates the effectiveness of pro-life laws. This summer it released a literature review showing that 20 of 24 studies found that public funding of abortion increased abortion rates. Other AGI research has demonstrated that parental-involvement laws and well-designed informed-consent laws also reduce the incidence of abortion. Unfortunately, research like that typically receives scant attention from the mainstream media.
