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Kim's glittering career prizes include the Golden Lion for best film at the 2012 Venice Film Festival for "Pieta", the same year he took Berlin's Silver Bear for "Samaritan Girl".
According to the South's Yonhap news agency, an actress whose identity is being withheld filed a complaint with prosecutors accusing Kim of slapping her in the face on the set of his 2013 film "Moebius", insulting her and forcing her into a nude scene.
She subsequently quit the movie, a thriller themed around incest, and her role was taken over by another actress.
"A criminal complaint has been filed against director Kim Ki-Duk and prosecutors have opened a probe into the case", the Seoul Central District Prosecutors' Office spokesman told AFP.
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He declined to elaborate, citing privacy.
Kim's agents denied the allegations as groundless, adding they would issue a detailed comment later.
"Moebius" was intially banned from being screened in South Korea on grounds of obscenity before being allowed to be released after some controversial scenes were removed.
It was screened out of the competition at the 70th Venice Film Festival.