In the statement, Weinstein admitted "making a pass" at the actor.
"Mr Weinstein acknowledges making a pass at Ms Thurman in England after misreading her signals in Paris," the statement said. "He immediately apologised."
After The New York Times' article was published, Weinstein had his publicist release a series of photos of he and Thurman posing together — photos that he said "demonstrate the strong relationship Mr Weinstein and Ms Thurman had had over the years".
Weinstein was involved in several of Thurman's best-known films, including her 1994 breakthrough Pulp Fiction and the Kill Bill series.
The statement insisted that there "was no physical contact during Mr Weinstein's awkward pass and Mr Weinstein is saddened and puzzled as to 'why' Ms Thurman, someone he considers a colleague and a friend, waited 25 years to make these allegations public, noting that he and Ms Thurman have shared a very close and mutually beneficial working relationship where they have made several very successful film projects together".
It also said "the pictures of their history tell a completely different story".
Commentators on social media have spoken out against Weinstein's response to these latest allegations.
