"Untrue," "disgraceful" and "tragic" were among their comments after Farrow, 28, repeated her allegations against Allen in a detailed open letter to the New York Times website during the weekend.
She also criticized Hollywood for honoring the 78-year-old "Blue Jasmine" and "Annie Hall" filmmaker with so many accolades.
The father and daughter have been estranged since Allen left Farrow's mother Mia in 1992 to pursue a romance with Farrow's adopted 19-year-old daughter, Soon-Yi Previn. Allen and Previn married in 1997 and have two adopted daughters of their own.
"Mr. Allen has read the article and found it untrue and disgraceful," Allen's publicist, Leslee Dart said in a statement to the New York Daily News Sunday.
"At the time, a thorough investigation was conducted by court-appointed independent experts," Dart said. "The experts concluded there was no credible evidence of molestation; that Dylan Farrow had an inability to distinguish between fantasy and reality; and that Dylan Farrow had likely been coached by her mother, Mia Farrow. No charges were ever filed."
"It is tragic that after 20 years, a story engineered by a vengeful lover resurfaces after it was fully vetted and rejected by independent authorities," Allen's lawyer, Elkan Abramowitz, told the Daily News. "The one to blame for Dylan's distress is neither Dylan nor Woody."
The Farrows first made the allegations against Allen during a custody battle over Dylan, her adopted brother Moses and her brother Ronan, the only biological child of Mia Farrow and Woody Allen, who has never been charged with any crime.
The Daily News reported Connecticut prosecutor Frank Maco said in 1993 he believed Allen molested his daughter, but decided not to charge him to avoid putting Dylan through the trauma of a trial. The statute of limitations for charging Allen has since run out, the report said.
"I love and support my sister and I think her words speak for themselves," Ronan, who is now an MSNBC personality, said on Twitter Sunday.