WASHINGTON — Several of the Republican Party’s most generous donors called on the Republican National Committee on Thursday to disavow Donald J. Trump, saying that allegations by multiple women that Mr. Trump had groped or made inappropriate sexual advances toward them threatened to inflict lasting damage on the party’s image.

To an elite group of Republican contributors who have donated millions of dollars to the party’s candidates and committees in recent years, the cascade of revelations related to Mr. Trump’s sexual conduct is grounds for the committee to cut ties with the party’s beleaguered standard-bearer, finally and fully.

“At some point, you have to look in the mirror and recognize that you cannot possibly justify support for Trump to your children — especially your daughters,” said David Humphreys, a Missouri business executive who contributed more than $2.5 million to Republicans from the 2012 campaign cycle through this spring and opposed Mr. Trump’s bid from the outset.

Bruce Kovner, a New York investor and philanthropist who with his wife has given $2.7 million to Republicans over the same period, was just as blunt. “He is a dangerous demagogue completely unsuited to the responsibilities of a United States president,” Mr. Kovner wrote in an email, referring to Mr. Trump.