Zito initially had wanted to skip the Preakness and go straight to the Belmont, but on Monday, Robert LaPenta, who owns Ice Box, said he was desirous of running in the Preakness, too.
"After talking to Mr. LaPenta, we concurred that Ice Box's race was tremendous, but we also knew it was a tough race," Zito said in a statement released through Churchill Downs. "We feel that we are better suited to wait and pass the Preakness and possibly go on to the Belmont and, hopefully, things work out. Also, we have more evaluation to do with Jackson Bend and will make a decision on his status for the Preakness on Monday."
Jackson Bend, also owned by LaPenta, finished 12th in the Derby.
Both Ice Box and Jackson Bend have remained at Churchill Downs since the Derby.
Ice Box had a tough trip in the Derby. He was caught in traffic twice in the final five-sixteenths of a mile and had to severely alter course both times. Because of that, he was seen as the primary challenger to Derby winner Super Saver in the Preakness.
Ice Box scored the biggest win of his career in his previous start, the Florida Derby.