The foundation that oversees the Bayreuth Festival appointed Katharina Wagner and her half-sister Eva Wagner-Pasquier, the great-granddaughters of Richard Wagner, to lead the annual opera event founded by the German composer, according to a statement from family member Wolf Siegfried Wagner.

The decision ends years of tussling over who should succeed Wolfgang Wagner, the 89-year-old father of Katharina and Eva. He stepped down as director of the festival in August after 57 years. The foundation’s choice is his preferred solution and a defeat for his niece Nike Wagner, 63, who joined forces with Paris Opera chief Gerard Mortier to bid for the post.

In a statement distributed to journalists at the town hall in Bayreuth, Germany, today, Wolf Siegfried Wagner described the selection process as “unworthy,” and said Nike Wagner’s joint bid with Mr. Mortier had not been impartially examined.

“That doesn’t prevent us from wishing Eva and Katharina much luck in their future work,” said the statement, written on behalf of the descendants of Wieland Wagner, Wolfgang’s late brother.

Katharina Wagner, 30, directed her first Bayreuth production last year, “Die Meistersinger von Nurnberg.” Eva Wagner-Pasquier, 63, is a consultant to the Aix-en-Provence opera festival.

“Of course I am sad about the outcome of the process,” Nike Wagner said in a separate statement. “I hope that my cousins will seize the initiatives that Gerard Mortier and I presented. I wish them much success in that.”