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The 37-year-old actor, whose June disappearance touched off wild speculation about her whereabouts, has appeared in the "X-Men" and "Iron Man" film franchises, attracting more than 62 million online followers in China.
Xinhua said an investigation by Chinese tax authorities found Fan had split her contract to evade taxes of 7.3 million yuan ($1.1 million) over payments for her role in "Air Strike", a film due to be released this year.
Fan and companies she represented also evaded 248 million yuan ($36 million) in additional taxes, Xinhua said, but it gave no details regarding this figure.
The tax bureau in the eastern coastal province of Jiangsu delivered its judgment to Fan on Sunday, levying fines of more than 596 million yuan ($86.7 million) for tax evasion and assessing overdue taxes of more than 288 million yuan ($42 million), Xinhua said.
In a letter posted on her official account on the Twitter-like platform Weibo, Fan said she fully accepted the authorities' decision, would overcome "all difficulties" to pay the penalties, and step up supervision of her companies.
"I'm ashamed of my behaviour and I apologise here to everyone," Fan wrote.
"Every bit of my achievement is inseparable from the support of the state and the people. Without the good policies of the Communist Party and the state, without the love of the people, there is no Fan Bingbing."
Xinhua said that under Chinese law Fan, as a first-time offender, would face no criminal charges if she complied with the judgement and paid all the money by an undisclosed deadline.
Reuters could not immediately reach Fan or a representative to seek comment. Xinhua said police had put a "restriction" on Fan's agent for attempting to conceal and destroy evidence during the investigations in June.
Fan dropped off the radar that month, amid reports that she was involved in the investigation, a vanishing act that prompted reports she had been detained.
On Wednesday, the South China Morning Post said Fan was released two weeks ago from "residential surveillance" at a "holiday resort" in Jiangsu used to investigate officials. She was transferred to Beijing for further investigation, the Post said, citing unnamed sources.
Since June, China has been investigating tax evasion in its film and television industry, following reports that some of its most famous actors have been accused of signing so-called "yin-yang" contracts, one of which sets out the real terms, while a second, with a lower figure, is meant for tax officials.
The State Administration of Taxation (SAT) said companies and individuals in the industry who voluntarily "rectify their behaviour" and pay back taxes evaded prior to December 31 will be exempt from administrative punishment and fines, Xinhua said.