Mr. Prince said that on Wednesday he had returned the original price of the Ivanka piece to the art adviser who had requested it. It’s unclear whether Ms. Trump herself or someone close to her bought the work, which uses an Instagram post with an image showing her getting her hair done. (In the Instagram post where she poses with the work, she thanks Mr. Prince and comments that she loves the piece.)

Ms. Trump, through a spokesman, declined to comment on Thursday. But a person in her circle, who was not authorized to speak about the matter because of the personal nature of her art purchases and collection, said the money was in the process of being returned by Mr. Prince.

Asked if he thought his disavowal would have any effect on the piece’s status as a legitimate Richard Prince work or on its market value, Mr. Prince said: “Whether it will affect anything is not the point. It’s a way of me saying to them I don’t want my work in your possession. I don’t want anything to do with your family.”

There is ample historical precedent for artists declaring works null and void, but not much evidence that they have the power to withdraw a work once it has fully entered the public realm. In 1963, for example, the sculptor Robert Morris, angered that the architect Philip Johnson was late in paying for a work, wrote a kind of affidavit negating the “aesthetic quality and content” of the piece. But both the piece and the manifesto are now in the collection of the Museum of Modern Art as Morris works.

Joshua Holdeman, a Manhattan art adviser and a former vice chairman at Sotheby’s, said he believed Mr. Prince’s excommunication of the work would probably not cause collectors or museums to treat it as illegitimate in the long run and he added that it might indeed increase its value.

“As far as the market is concerned, if an artist says a work isn’t by him, but it’s clear that he made it and presented it as his work, well it kind of is what it is,” Mr. Holdeman said. “My intuition about this is that when history plays out, this will probably end up being a more culturally rich object than if this whole episode hasn’t happened.”