WASHINGTON — Congressional Democrats on Thursday began giving away some of the thousands of dollars in campaign contributions they had received from Harvey Weinstein, a wealthy Hollywood producer, moving to distance themselves from him after revelations he had reached at least eight settlements with women accusing him of sexual harassment.

Senators Patrick J. Leahy of Vermont, Richard Blumenthal of Connecticut, Martin Heinrich of New Mexico and Elizabeth Warren of Massachusetts each said they would transfer money to charity in amounts equal to donations they had received from Mr. Weinstein. Mr. Leahy was planning to donate $5,600, Mr. Blumenthal and Mr. Heinrich $5,400 and Ms. Warren $5,000. Some of them were planning to give to groups that advocate for women who are the victims of domestic violence.

With the four senators ridding themselves of Mr. Weinstein’s contributions, other Democratic lawmakers were expected to follow suit on Friday in order to mitigate a deeply embarrassing story.