In a follow-up New York Times op-ed, Allen repeated his denial and launched a furious attack on Mia Farrow, denouncing her as "more interested in her own festering anger than her daughter's well-being".
King asked why people should believe her after 25 years of silence.
In the wake of renewed interest in sexual assault allegations against her estranged stepfather, Dylan Farrow will appear on CBS to discuss the current situation.
"All I can do is speak my truth and hope - hope that somebody will believe me rather than just hearing", she said.
"I didn't like it when I had to get in bed with him under the sheets when he was in his underwear", she wrote.
The allegations first came to light in the early '90s during Allen's very public and acrimonious split with Farrow's mother, Mia.
Baldwin's tweets came after actor Timothee Chalamet, the breakout star of Call Me by Your Name, announced on Instagram that he was donating his salary from his role in Allen's most recent film, A Rainy Day in NY, to charities that fight sexual abuse and harassment.More news: Gov. Chris Christie signs bump stock ban on way out of office
"I want to be worthy of standing shoulder to shoulder with the courageous artists who are fighting for all the people to be treated with the respect and dignity they deserve".
The allegations have resurfaced amid the #MeToo and Time's Up Movements in Hollywood, exposing sexual abuse in the industry.
"I don't want to profit from my work on the film, and to that end, I am going to donate my entire salary to three charities: TIME'S UP, The LGBT Centre in NY, and RAINN", he wrote.
A number of actors have recently distanced themselves from the director.
Dylan Farrow's remarks were aired today as a prelude to what CBS This Morning calls her first on-camera discussion of the issue. "He then sexually assaulted me", Farrow wrote in a 2017 op-ed published in The Los Angeles Times. He was investigated at the time, but never charged. Citing a lack of evidence, police did not charge Allen in connection with Dylan Farrow's accusations.
Allen remains with Soon-Yi and the couple have two children.