James Franco addressed the sexual misconduct claims circulating about him on social media Tuesday night, telling late-night host Stephen Colbert that "the things I heard on Twitter are not accurate." Colbert had mentioned the criticisms raised Sunday by actress Ally Sheedy in a series of since-deleted tweets — claims that were then followed by separate allegations by multiple women.

"I have no idea why [Sheedy] was upset. She took the tweet down. I don't know, I can't speak for her," he told Colbert toward the end of their interview promoting Franco's film The Disaster Artist. "The others — look, in my life I pride myself on taking responsibility for things that I've done. I have to do that to maintain my well-being. I do it whenever I know that there is something wrong or needs to be changed."

"The things that I heard that were on Twitter are not accurate," he added, "but I completely support people coming out and being able to have a voice, because they didn't have a voice for so long. So, I don't want to shut them down in any way."

Franco's comments come several days after the Golden Globes award ceremony, where he won for best actor in a comedy or musical. During the broadcast, his evident support for "Time's Up," an initiative seeking to end sexual harassment and gender inequality in the workplace, prompted disgust from Sheedy and others.

"James Franco just won," Sheedy, whom Franco directed in a 2014 off-Broadway show, said on Twitter. "Please never ever ask me why I left the film/tv business."

In an earlier tweet, Sheedy had asked: "Why is James Franco allowed in?"

Both tweets, which lodged no specific allegations, have since been deleted, but at least two other women posted claims against the actor and director.

Filmmaker Sarah Tither-Kaplan alleged a contract she signed with Franco regarding nudity in two of his films was exploitative, and actress Violet Paley addressed a tweet to Franco, saying, "Remember the time you pushed my head down in a car towards your exposed penis & that other time you told my friend to come to your hotel when she was 17?"

"A couple weeks ago, James offered me & a few other girls an overdue, annoyed, convenient phone 'apology,' " Paley later tweeted, adding: "I don't accept."

Neither allegation has been independently confirmed by NPR.

Still, the simmering controversy was enough to dissuade The New York Times from holding an event featuring Franco. The paper canceled that event, which had been scheduled for Wednesday.

"The event was intended to be a discussion of the making of the film, 'The Disaster Artist.' Given the controversy surrounding recent allegations, we're no longer comfortable proceeding in that vein," the Times explained in a statement to The New York Daily News.

Franco remains scheduled to make another late-night appearance Wednesday, on Late Night with Seth Meyers on NBC.

In Tuesday night's conversation with Colbert, Franco reiterated his support for "Time's Up," saying he backs the drive for pay equity in the workplace, "which just means people that are underrepresented — women and people of color, people in the LGBT community — get leadership positions, that they fill all positions that they've been deprived of."

Then he spoke specifically of the claims against him.

"The way I live my life, I can't live — if there's restitution to be made, I will make it. So, if I've done something wrong, I will fix it. I have to. I think that's how that works. I don't know what else to do," Franco told Colbert.

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