Trying to salvage their case against Robert K. Kraft, the owner of the New England Patriots, for solicitation of prostitution, prosecutors in Florida on Tuesday appealed a lower court decision that had thrown out video evidence.

In May, a judge in Palm Beach County agreed with Mr. Kraft, whose lawyers argued that video showing the N.F.L. team owner and other patrons of a day spa in Jupiter, Fla., was improperly obtained by undercover video cameras installed there.

The Florida state attorney general, taking up the case for the state attorney in Palm Beach County who charged Mr. Kraft and two dozen others with solicitation of prostitution, asked an appeals court to overturn that decision, arguing that the police in the case followed established procedures for obtaining a warrant to install the cameras. A warrant must “be predicated on a showing of probable cause, and be particularized as to the place to be searched and items to be seized,” the state attorney general wrote in a 52-page brief with the Fourth District Court of Appeal of Florida. “This warrant satisfied all three requirements.”

Mr. Kraft’s lawyers also argued that patrons in the spa who were not under suspicion of soliciting prostitution, and who were videotaped without their knowledge, had their privacy violated.