The festival has always been run by the Wagner family
At a news conference on Thursday he told reporters that the festival's board of directors had agreed to put discussion of his replacement on hold until the autumn.
"Negotiations must continue in hopes of finding a constructive solution," said Wolfgang Wagner.
The move marks a cooling in the simmering dispute over the future of the world-famous opera house.
'Lifetime contract'
Earlier this year, the board tried to force Wolfgang Wagner to step down in favour of his estranged daughter Eva Wagner-Pasquier.
But so far he has refused to relinquish the position, arguing that he holds a lifetime contract with Bayreuth.
Eva Wagner-Pasquier has since said she is not interested in the position as long as her father refuses to leave.
Another contender is Wolfgang Wagner's niece Nike, who has teamed up with director of the Stuttgart State Opera Klaus Zehelein to apply for the position.
Plans
Wolfgang Wagner's directorship has increasingly been criticized as too conservative, and some singers and musicians have complained about what they call his autocratic style - and his tendency to offer only one-year contracts.
The director disputed the accusations again at Thursday's press conference, citing plans for a new staging of Tannhauser by French director Philippe Annaux scheduled for 2002.
"I only think about the future of Bayreuth," he said.
Richard Wagner founded the Bayreuth festival in 1876, believing that the out-of-the-way Bavarian village would be an appropriately serious and spiritual home for his works.
Wagner died before the festival was a decade old and its management passed to his widow, Cosima, and later to his children and grandchildren.
Wolfgang Wagner is perceived to have done much in the immediate post-war period to have distanced the festival from the Nazi associations of 1933-1945.