Critics say China's late-1970s family-planning law, which restricts most couples to one child, is selectively and sometimes brutally enforced, while the wealthy and well-connected are easily able to pay the fines levied for extra offspring.
But in recent days some users of China's popular online social networks have directed their anger at the policy itself, rather than Zhang, with some hoping the attention heaped on his case may hasten the eventual demise of the law, which authorities have recently moved to relax.
Guo Chengxi confirmed reports that it demands a total of one billion yuan (USD 164 million) from the director of "Red Sorghum" and "Raise the Red Lantern", half in compensation for public resources, and half in punitive damages.
"Right now, in China, this phenomenon of wealthy people having more than one child is very serious," she said, adding they decided to take action against Zhang because he "represents a typical case" of an elite trying to skirt the one-child law.
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"The rich have become increasingly audacious by violating the family planning policy just because they are rich enough to pay the fine... And they take an extra share of resources from society," Jia was quoted as saying in a front-page report in the government-run China Daily.
The court might not accept the case, the newspaper added.
Zhang, one of China's best-known filmmakers and the director of the opening and closing ceremonies at the 2008 Beijing Olympics, had faced rumours for months that he had fathered as many as seven children with several different women.
He acknowledged that he has two sons and a daughter with his current wife, as well as another daughter with his ex-wife.
The one-child policy was put in place to control China's booming population, and officials say it has been key to the country's rising prosperity.