Democratic senators have given campaign donations from movie producer Harvey Weinstein to rape crisis centers and organizations that support sexual harassment victims in recent days, as the politicians try to distance themselves from allegations that the disgraced Hollywood mogul sexually preyed upon women.

According to their press offices, California Sens. Kamala Harris and Dianne Feinstein donated $5,000 and $10,000, respectively, to women’s organizations. Connecticut Sen. Richard Blumenthal gave $2,700 to the Connecticut Alliance to End Sexual Violence, and New York Sen. Kristin Gillibrand gave $11,800 to RAINN, the national sexual assault hotline.

Malinda Williams, executive director of the New Mexico nonprofit Community Against Violence, said that Sen. Martin Heinrich — who donated $5,400 to the organization from his Weinstein contributions — has always been a staunch supporter of her group’s work.

“His support means a lot to us but this donation is substantial to our agency and we need this kind of money to be able to keep doing what we do,” Ms. Williams said in a phone interview.

Mr. Weinstein has been a top contributor to Democratic candidates and the Democratic Party, with some donations totaling more than $1 million since 2000, according to analysis by Business Insider. Some of his largest donations went to the Democratic campaigns of President Barack Obama and presidential nominee Hillary Clinton, who reportedly said she was “shocked and appalled” by Mr. Weinstein’s alleged behavior.

Reports emerged Tuesday that Mr. Weinstein is accused of raping three women and sexually harassing Oscar-winning actresses Angelina Jolie and Gwyneth Paltrow, among others. The New York Times broke the story this month that the movie producer has settled several lawsuits alleging sexual harassment over the years.

Sen. Chris Murphy, Connecticut Democrat, urged his colleagues Sunday to refund any political donations from Mr. Weinstein.

“This was a high-profile individual who did some truly awful things,” Mr. Murphy said on CNN. “And people that took money from him should probably give it back.”

The New Jersey Coalition Against Sexual Violence recently received a $7,800 donation from Sen. Cory Booker, a little less than half of the total amount of contributions he received from Mr. Weinstein since 2000, according to the Business Insider analysis.

“This is a really important contribution because what it shows is the importance of putting our money where our mouths is,” said Patricia Teffenhart, the coalition’s executive director. “What makes this donation so powerful to us is that we need both legislative and financial support in order to help our rape crisis centers serve the 10,000 survivors and loved ones that they serve every year.”