Last year, some prominent scholars and policy advisers started a major effort to push central officials to fundamentally change or repeal a law that generally punishes families for having more than one child. That push comes as economists point out that China’s economic growth rate is likely to slow because its pool of cheap, young workers is dwindling as the population ages.

The 2010 national census showed that the average birthrate for a Chinese household was 1.181; it was lower in cities and higher in rural areas. Some scholars say that number is extraordinarily low, and the real figure is probably a bit higher.

The family planning regulations are prone to abuse because local officials are often evaluated by their superiors based on how well they keep down the populations of their areas. There have been well-known cases of forced abortions or sterilizations across China. Last year, Chinese Internet users sympathized with the plight of Pan Chunyan, who said she had been abducted by officials in Daji Township when she was eight months pregnant with her third child. The officials forced her to have an abortion at a hospital. In June 2012, another woman, Feng Jianmei, was forced to abort a 7-month-old fetus in Shaanxi Province, in a case that also ignited national outrage.

Parents in other parts of China have accused local family planning officials of abducting babies who are considered “extra” children in a household and selling them to orphanages, sometimes for $3,000 per baby.

The Beijing News report said Mr. Wu, the lawyer, obtained data showing that Jiangxi Province had collected the most in fines of the 19 provinces that replied to him; it amassed $554 million in 2012. Sichuan was second with $400 million, and Fujian was third with $340 million. The provinces that collected the least were Qinghai, with $572,000, and Ningxia, with about $2 million. Both have low populations compared with most other provinces, and they are also home to many rural residents and ethnic minorities, who have more leeway in the number of children they can have without incurring fines.