Woody Allen has accused Dylan Farrow, his adoptive daughter, of "cynically" using Hollywood's "Time's Up" movement to renew her claims of sexual assault.

Allegations against the Oscar-winning director were dropped by state prosecutors in 1993 but Farrow repeated them in an open letter in 2014, claiming he had molested her in the family home when she was 7.

On Thursday, Farrow gave her first public TV interview about the claims, saying she hoped that appearing on camera would convince people she was telling the truth.

"He's lying and he's been lying for so long," Farrow, 32, told CBS, adding, "I want to speak out. Literally."

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Allen, 82, issued an angry rebuke, accusing Farrow of using the Harvey Weinstein scandal and its fallout in Hollywood to boost her own platform.

"Even though the Farrow family is cynically using the opportunity afforded by the Time's Up movement to repeat this discredited allegation, that doesn't make it any more true today than it was in the past," he said in a statement to CBS.

"I never molested my daughter - as all investigations concluded a quarter of a century ago."

At the time, Allen suggested Farrow had been coached to make the allegation by her mother, Mia Farrow, with whom Allen had had a relationship from 1979 to 1992. Allen claimed she had been angry "during a contentious break-up".

Months earlier, Mia Farrow had found pictures of her adoptive daughter, Soon-Yi Previn, posing nude, in Allen's apartment.

Allen confessed to having an affair with Previn and the pair married in 1997.

During her interview, Dylan Farrow said: "What I don't understand is how is this crazy story of me being brainwashed and coached more believable than what I'm saying about being sexually assaulted by my father?

"I loved my father ... And that doesn't obviously take away from what he did. But it does make the betrayal and the hurt that much more intense."

She also claimed that Allen had behaved inappropriately on other occasions, coaxing her to "get into bed with him when he had only his underwear on".

The allegations were reported to authorities but Frank Maco, the state prosecutor in the case, decided Farrow was too fragile to face a high-profile trial, despite finding "probable cause" to charge Allen. Farrow has now said that she wants to testify in a court of law.