Angelina Jolie speaking at the Global Summit to End Sexual Violence in Conflict in 2014
The A-list actresses alleged the incidents had occurred during their early years in the industry. They are among several actresses - including Ashley Judd and Rose McGowan - to have made harassment claims against Weinstein.
Yesterday, the movie mogul also denied serious sexual assault allegations in The New Yorker magazine.
Weinstein's wife Georgina Chapman also announced that she was leaving him. In a statement to People magazine, asking for privacy for herself and her children, she said: "My heart breaks for all the women who have suffered tremendous pain because of these unforgivable actions."
The allegations from Paltrow and Jolie came in the New York Times.
Jolie said: “I had a bad experience with Harvey Weinstein in my youth, and as a result, chose never to work with him again and warn others when they did. This behaviour towards women in any field, any country is unacceptable.”
Paltrow alleged that, after she was cast as the lead in Emma, Weinstein summoned her to his hotel suite, where he placed his hands on her and suggested massages in his bedroom.
She told the paper: "I was a kid, I was signed up, I was petrified."
Asia Argento was one of the actors to go on the record with The New Yorker, claiming she feared speaking up before because it would kill her career.
Weinstein's spokesman issued a statement in response to The New Yoker allegations. She said: “Any allegations of non-consensual sex are unequivocally denied by Mr Weinstein. Mr Weinstein has further confirmed that there were never any acts of retaliation against any women for refusing his advances.
"Mr Weinstein obviously can't speak to anonymous allegations, but with respect to any women who have made allegations on the record, Mr Weinstein believes that all of these relationships were consensual. Mr Weinstein has begun counselling, has listened to the community and is pursuing a better path.
"He will not be available for further comments, as he is taking the time to focus on his family, on getting counselling and rebuilding his life.”
The Weinstein Company’s Board has also been under pressure after McGowan called for the entire board to resign.
The actress told The Hollywood Reporter: "I’m calling on the board to resign effective immediately. And for other men to stop other men when they are being disgusting."
And on Twitter, yesterday, she wrote: "TWC [The Weinstein Company]. You don't get to change your company name and be done with it. Every man there has the blood of sorrow on their hands. You are dirty."
TWC You don’t get to change your company name & be done with it. Every man there has the blood of sorrow on their hands. You are dirty.— rose mcgowan (@rosemcgowan) 10 October 2017
The actress also urged her followers to sign a petition calling for the dissolution of the company. It currently has more than 5,500 signatures.
The Weinstein Company's Board of Representatives issued a statement last night. It said: "The Weinstein Company’s Board of Representatives - Bob Weinstein, Lance Maerov, Richard Koenigsberg and Tarak Ben Ammar - are shocked and dismayed by the recently emerged allegations of extreme sexual misconduct and sexual assault by Harvey Weinstein. These alleged actions are antithetical to human decency. These allegations come as an utter surprise to the Board. Any suggestion that the Board had knowledge of this conduct is false.
"We are committed to assisting with our full energies in all criminal or other investigations of these alleged acts, while pursuing justice for the victims and a full and independent investigation of our own."
The latest developments came after a number of stars also spoke out in support of the actresses making the allegations.
George Clooney, whose big break as a movie actor came in Weinstein's From Dusk Till Dawn, branded the alleged behaviour "indefensible" in a lengthy interview with The Daily Beast.
Hillary Clinton - whose Democratic Party has received substantial donations from Weinstein - also retweeted a statement on Twitter, saying she was "shocked and appalled by the revelations".
Statement from Secretary Clinton on Harvey Weinstein: pic.twitter.com/L1l2wl9l0I— Nick Merrill (@NickMerrill) 10 October 2017