The allegations have been levelled by Donya Fiorentino, the actor's former wife and Gulliver's mother.
Gulliver, 20, criticised "clickbait journalism" and accused his mother of perpetuating an alleged domestic violence incident that never happened.
"It has been troubling and painful to see that these false allegations against my father being written about again, especially after this was all settled years ago. There is good reason that these specific articles and accusations subsided years ago.
"I have grown up in the world we are accustomed to now, where people are guilty until proven innocent. It's a shame to see that 'clickbait journalism' or judgement by headline, is designed to make one jump to conclusions without receiving the full range of fact that may be detailed in a piece, whether it be online or otherwise," he said in a statement to The Hollywood Reporter.
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"In the case of my father, there is only innocence. There never has been any guilt... My father is my one and true guiding light. My only hero. He is the man I aspire one day to become. If I could only become even half as great and half as pure. I was granted the good graces of his fatherhood as a child to be raised by him and only him. For that I am eternally grateful every hour of every day. I owe him the world and I owe him my life...
After Oldman's Best Actor win at the Oscars, Fiorentino took to Twitter to accuse him again.
"Congratulations, Gary and congratulations to the Academy for awarding not one but two abusers with Oscars (sic), Fiorentino said, referencing Oldmans win as well as Kobe Bryant's for Dear Basketball.
Last month, Fiorentino, who was married to Oldman from 1997 to 2001, had called her marriage to the actor a "nightmare" and claimed that he hit her with a telephone in front of their young children long time back .
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