The schedule, the Austrian conductor said on Saturday, was "impractical", and starting at such an early hour "would mean the singers would have to wake up at 3:00 am in order to be ready".
He also withdrew from conducting performances of Mozart's two other operas written with librettist Lorenzo Da Ponte, "Don Giovanni" and "Le Nozze di Figaro", scheduled for 2014 and 2015.
The decision is a major blow to organisers since works by Mozart, who was born in Salzburg, have always formed the core repertoire of the Austrian city's summer festival, which in 2013 runs from July 19 to September 1.
Artistic director Alexander Pereira issued a statement on Monday calling his compatriot Welser-Moest's decision "completely disproportionate", although he admitted that the 11:00 am start had not been discussed.
Perreira said his proposal to start rehearsing "Cosi" several weeks before the planned premiere on August 21 had been rejected by Welser-Moest "because he simply had to go on holiday".
"The real reason for cancelling is probably that two people who at one time worked very intensively together over many years have now grown apart," Perreira said.
The two men worked very closely and successfully in the past at the Zurich opera, where Perreira was general manager and Welser-Moest general music director.
Perreira told the Kurier daily that he would soon be able to present a replacement for Welser-Moest for the Da Ponte cycle, saying it was possible that he would engage three different conductors.
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