Not all have led to formal charges and even fewer to convictions, but Dr. Hänel and other doctors see a trend that they say aims to prevent them from providing a legally allowed medical procedure.

“I can’t believe that in this day and age the language and mind-set of the time when abortions were illegal continue to play a role in a country that is otherwise viewed by the rest of the world with respect,” Dr. Hänel wrote on March 19 in an open letter to Ms. Merkel. “I am ashamed and I hope that we can resolve this problem.”

This is not the first time Germans have struggled with the issue of abortion. The procedure was illegal in West Germany until the 1970s, when women took to the streets to demand the right to decide what happens with their bodies. In 1974, a law was passed legalizing abortion in the first trimester, but the country’s highest court overturned that ruling the following year.

A compromise requiring permission from a doctor in order to be allowed an abortion was further eased in the 1990s, after East Germany — where abortion was allowed in the first 12 weeks of pregnancy — was absorbed into the West, leading to the current legal agreement. Under that arrangement, abortion is a crime, but will not be prosecuted in the first 12 weeks if a woman undergoes counseling and a three-day waiting period.

In neighboring Austria, Christian Fiala, a gynecologist, has advertised for years that his clinic offers abortions. “Unwanted pregnancy?” reads a billboard in the University station of Vienna’s subway that includes his clinic’s name and telephone number. A decade ago, he began collecting the names of German doctors who perform abortions and publishing them on his website, which is based in Austria and therefore not subject to German restrictions.

“Information is absolutely essential, because women who find themselves unexpectedly pregnant need information urgently,” Dr. Fiala said. “This has nothing do with advertising that would make it easier for a woman to decide to have an abortion just because she sees a poster somewhere. That idea is not only completely absurd, it is pretty sexist.”