The U2 frontman composed the score for the show alongside bandmate The Edge and the pair appeared on the season finale of American Idol on Wednesday night to perform 'Rise Above'.
"I promise [the show has] not been cancelled, and we're very excited about it," he told reporters after the broadcast.
"It's almost there - it will be there by opening night."
Bono admitted earlier in the month that he agreed with negative reviews the show had received from critics before its overhaul.
He also explained that revisions were necessary because "the whole was not greater than the sum of the parts".
The Broadway musical, which opens on June 14, has experienced a variety of difficulties during production including a change of director, alleged safety violations and injuries to cast members.
Watch Bono and The Edge perform 'Rise Above' from Spider-Man: Turn Off the Dark below: