Film director Woody Allen has denied molesting his daughter and launched a furious attack on his ex-partner Mia Farrow, blaming her for the abuse allegations.

In a nearly 2000-word open letter in The New York Times, Allen castigated his former partner over shocking allegations detailed by their daughter Dylan in the paper last week.

“Of course, I did not molest Dylan,” he wrote, adding that he had “loved” the girl he adopted with Mia during their 12-year relationship that broke up in enormous acrimony.

“I… hope one day she will grasp how she has been cheated out of having a loving father and exploited by a mother more interested in her own festering anger than her daughter’s well-being.”

Allen also addressed reports that Ronan Farrow may be Frank Sinatra’s son, not his.

“Granted, he looks a lot like Frank with the blue eyes and facial features, but if so what does this say? That all during the custody hearing Mia lied under oath and falsely represented Ronan as our son?” the director asked.

“Even if he is not Frank’s, the possibility she raises that he could be, indicates she was secretly intimate with him during our years. Not to mention all the money I paid for child support. Was I supporting Frank’s son?”

Allen said he raised the matter to “call attention to the integrity and honesty of a person who conducts her life like that,” referring to the Mia.

In an open letter on a New York Times blog, 28-year-old Dylan Farrow said on Saturday she was molested by Allen as a seven-year-old, detailing the alleged abuse for the first time in her own words.

Dylan suggested that other abuse may have started even earlier, saying: “For as long as I could remember, my father had been doing things to me that I didn’t like.”

The unproven allegations first emerged in the aftermath of Allen’s split with Mia in 1992.

Allen, 78, left Mia after starting a relationship with the actress’s adopted daughter from a previous marriage, Soon-Yi Previn.

A New York judge who presided over the 1994 custody battle between Allen and Mia ruled that the abuse allegations were inconclusive, but at the same time lambasted the director as “self-absorbed, untrustworthy and insensitive”.

And a Connecticut police investigation did not result in any charges.

“Could it be any clearer? Mr Allen did not abuse Dylan; most likely a vulnerable, stressed-out seven-year-old was coached by Mia Farrow. This conclusion disappointed a number of people,” Allen wrote, referring to himself in the third person.

Dylan accused Hollywood of sweeping Allen’s alleged crimes under the carpet by honouring his films.

Allen was celebrated with a lifetime achievement award at the Golden Globes in January and his latest movie Blue Jasmine, starring Cate Blanchett, is up for three Oscars at the Academy Awards.

Writing in the Times, the director said experts from Yale University’s child sex abuse clinic at the time concluded he had not molested Dylan.

Dylan added “a few little added creative flourishes that seem to have magically appeared during our 21-year estrangement,” Allen wrote.

It was his second denial since Dylan’s post was published. On Sunday, his publicist called the allegations “untrue and disgraceful”.