China's top film director Zhang Yimou has said he violated the country's one-child policy because of the traditional belief that having multiple children would lead to greater prosperity, state media said.

After months of rumours that he had fathered as many as seven children with several different women, Zhang issued an apology on December 1 acknowledging that he has two sons and a daughter with his current wife, and another daughter with his ex-wife.

Zhang, who faces an official penalty largely based on his and his wife's income in the years before each child was born, also claimed that one year he only earned $450.

In an interview with the official Xinhua news agency Sunday, the director of the 2008 Beijing Olympics opening and closing ceremonies said he broke the law because his father told him before dying that he wanted a grandson to "carry on the family name".

"Traditionally my parents and I thought the more children one has, the more prosperous the family would be," he was quoted as saying.

Previous Chinese media reports have speculated the fine could be as high as 160 million yuan ($26 million) and some lawyers are demanding one billion yuan from the director of "Red Sorghum" and "Raise the Red Lantern".

But according to the documents Zhang provided, his total income in 2000 was only 2,760 yuan (now $450), Xinhua said.

"A film director's income is irregular -- there are good years and there are bad years," Zhang was quoted as saying.

His total income in the relevant years came to 3.6 million yuan, the report said, adding that his wife is a housewife.

That will put the fines at more than seven million yuan, still the highest ever known for such offences, a lawyer in Beijing estimated, according to Xinhua.

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.

But with demographic experts warning of a labour shortage within the next two decades, China's Communist Party leaders last month moved to expand the exceptions to the policy after a key meeting in Beijing, allowing couples to have two children if one of the parents is an only child.

Zhang has come under mounting criticism for taking advantage of his fame and wealth, but said his family had suffered because they had broken the rules, according to the report.

"We were hiding here and there as 'extra-birth guerillas'", Zhang said, referring to a TV comedy in the 1990s about a couple who went on the run to have multiple babies.

"My fault has negatively affected my children's childhood significantly," he added.