ROME — Italy’s highest court on Tuesday ordered a new trial in the sensational case of Amanda Knox, an American exchange student accused of murdering her 21-year-old roommate, Meredith Kercher of Britain, in 2007. The judges’ announcement that earlier acquittals had been overturned was greeted by a shocked silence in the courtroom here. The ruling by the Court of Cassation means that the case against Ms. Knox and her former boyfriend, Raffaele Sollecito, will be reheard at a new appeals court in Florence either later this year or in 2014. The two were initially convicted in a trial that divided public opinion internationally but were acquitted on appeal 18 months ago. Prosecutors then challenged that acquittal. The decision opened a further tangled and dramatic chapter in a long-running case whose youthful protagonists, sometimes lurid detail and courtroom spectacle has fascinated many people in the United States, Britain and the rest of Europe.