The Hollywood mogul, 65, issued a lengthy statement after the article was published, acknowledging that his behaviour with colleagues had caused a "lot of pain" and apologising for it.
The report cites accounts of several women, including former employees and actor Ashley Judd, who said she was called to his hotel suite for what she thought would be a business breakfast. She said Weinstein appeared in a bathrobe and asked whether he could give her a massage or she could watch him shower.
The allegations against the producer span three decades and both the companies he worked with.
Weinstein is co-chairman of The Weinstein Company, the studio behind Oscar-winning films such as "Silver Linings Playbook", "The King's Speech" and "Django Unchained". Before forming TWC, he had co-founded Miramax Films.
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The producer said in his statement that he planned to take leave of absence without specifying when.
"I came of age in the '60s and '70s, when all the rules about behavior and workplaces were different. That was the culture then. I have since learned it's not an excuse, in the office -- or out of it," Weinstein said.
While he apologised for his behaviour, Weinstein also made it clear that he would sue The New York Times for "reckless reporting", according to New York Post's Page Six.
"What I am saying is that I bear responsibility for my actions, but the reason I am suing is because of the Times inability to be honest with me, and their reckless reporting. They told me lies. They made assumptions.
He added that the newspaper was so fearful that the story would be killed that they went ahead and posted it without checking all they had with him and his team.
Weinstein has hired Charles J Harder, the LA attorney who won a USD 140-million case for Hulk Hogan from Gawker after the site posted a sex tape, to prepare a lawsuit against The Times.