Reports had circulated online since May that Zhang, 62, had fathered seven children from two marriages and relationships with two other women. The People's Daily newspaper, the ruling Communist Party's mouthpiece, had reported that Zhang could face a fine of up to 160 million yuan ($26 million). People caught breaking China's family planning policy must pay a "social compensation fee" based on their annual income.
In his first response to the reports, Zhang's office issued an open letter through its verified microblog account on the Twitter-like Sina Weibo site late Sunday denying that the director had seven children but admitting that he and his wife have two sons and a daughter in violation of China's one-child limits.
Zhang and his wife "expressed their sincere apology to the public for the negative social impact that this has created," the letter said.
The letter said Zhang and his wife were willing to be investigated by the family planning committee in Chen's hometown, the eastern city of Wuxi, and would accept whatever penalty the couple might incur. It did not provide details on how the couple had been able to evade family planning authorities thus far.
The family planning office of Wuxi's Binhu district said in their online statement that the couple had had three children in 2001, 2004 and 2006 in Beijing without first seeking approval from family planning authorities, and out of wedlock. They obtained a marriage certificate in 2011, the statement said.
Family planning policies and the fines for breaking them vary from city to city. Some consider unmarried childbearing illegal.
The statement quoted an unnamed spokesman as saying the office hoped Zhang and Chen would continue to cooperate with family planning authorities and truthfully report their income at the time.
Zhang's office rejected reports that he had fathered more children. It said unidentified individuals with "ulterior motives" had sent people to follow Zhang's children and photograph them and that Zhang's office reserved the right to take legal action.
Known to many as China's one-child policy, the rules limit most urban couples to one child and allow two children for rural families if their firstborn is a girl. The government introduced the policy in 1979 as a temporary measure to curb a surging population, but it is still in place despite being reviled by many citizens.
Last month, the party announced that it would allow couples to have two children if one of the parents is a single child, the first substantial easing of the one-child policy in nearly three decades.
Zhang's 25-year career has made him one of Chinese cinema's top names. He is part of China's "fifth generation" of directors those who gained attention in the West as their country emerged from economic and political isolation in the 1980s. Many of his films portray gritty rural life. In recent years, he has experimented with big-budget blockbusters, such as the 2011 "The Flowers of War," with an estimated $94 million budget.
Zhang also designed the opulent opening and closing ceremonies for the 2008 Beijing Olympics.
AP writer Louise Watt contributed to this report.