The organizer behind an honor named for Justice Ruth Bader Ginsburg, a lifelong champion of women’s rights and liberal causes, is canceling the award ceremony scheduled for April after facing blistering criticism from her family and friends over several of this year’s planned recipients.

Justice Ginsburg helped establish the award in 2019, the year before she died. It was originally intended for “women who exemplify human qualities of empathy and humility,” but four of the five intended recipients this year are men. Among them are Elon Musk, the tech entrepreneur who frequently lobs tirades at perceived critics; Rupert Murdoch, the tycoon whose empire helped give rise to conservative news media; and Michael R. Milken, the financier who was a face of corporate greed in the 1980s and served nearly two years in prison before becoming a philanthropist.

“The last thing we intended was to offend the family and friends of R.B.G.,” Julie Opperman, the chairwoman of Dwight D. Opperman Foundation, which awards the prize every year, said in a statement on Monday. She added: “The foundation is not interested in creating controversy. It is not interested in generating a debate about whether particular honorees are worthy or not.”

Ms. Opperman explained that the reason for including men as recipients this year was to reflect and uphold Justice Ginsburg’s “teachings regarding equality.” The foundation “did not consider politics” but focused on selecting leaders who “have made significant contributions to society,” she said.

Before the foundation released the statement, the children of Justice Ginsburg had demanded that their mother’s name be removed from the prize, which until this year was called the Justice Ruth Bader Ginsburg Woman of Leadership Award.

Her daughter, Jane C. Ginsburg, a law professor at Columbia, said the choice of winners this year was “an affront” to the values the justice stood for.

James S. Ginsburg, her son and the founder of Cedille Records, a classical music recording company, said on CNN over the weekend that celebrating Mr. Musk and Mr. Murdoch with the justice’s name amounted to “desecration of my mother’s memory,” and he vowed to “fight” the decision.

The intended recipients this year, who also include the businesswoman Martha Stewart and the actor Sylvester Stallone, were scheduled to be honored with the renamed Justice Ruth Bader Ginsburg Leadership Award at a gala next month at the Library of Congress. A spokesman for the Opperman Foundation confirmed on Monday night that the ceremony had been canceled, but said no decision had been made on whether those selected would still receive the award. In its statement, the foundation said it would “reconsider its mission” and assess “how or whether to proceed in the future.”

Past recipients include Queen Elizabeth II, the fashion designer Diane von Furstenberg and the actress and singer Barbra Streisand.

Over the nearly three decades she spent on the court, Justice Ginsburg emerged as a progressive voice, on the winning side in cases involving abortion, affirmative action and gender equality. When she found herself in the minority, she did some of her most notable work in dissent.

“Justice Ginsburg spent her life fighting to combat discrimination in all its many forms, to empower women to have control over their own destinies and to open up opportunities for persons from all walks of life,” said Amanda L. Tyler, one of the justice’s former law clerks, who co-wrote a book with Justice Ginsburg about the judge’s career and is now a law professor at the University of California, Berkeley.

“Any award bearing Justice Ginsburg’s name should honor that great legacy,” she added.