Prosecutors and a lawyer for Kercher's family argued that appeals court judges "lost their way" in analyzing the evidence and that Knox and Sollecito should be retried for Kercher's murder.
"We feel that Amanda and Raffaele are guilty and were in the room with Rudy Guede," Francesco Maresca, lawyer for the Kercher family, said as he entered the Corte di Cassazione, Italy's supreme court, in Rome.
Guede, an Ivory Coast drifter, has also been convicted in the 2007 murder and is serving a 16 year prison term.
Since her 2011 release from prison, Knox has resumed her life in Seattle, taking classes and spending time with her family and boyfriend, James Terrano.
Her memoir, "Waiting to Be Heard," published by HarperCollins, will be released April 30. She reportedly received an advance of $4 million for the book.
Knox's first interview since she was freed will air during a primetime special on Tuesday, April 30 at 10 p.m., ET on the ABC Television Network.