The 24-year-old American from Seattle, Wash. was convicted by a lower court of sexually assaulting and murdering her British roommate, Meredith Kercher while they were studying in Perugia in 2007.
Knox's former boyfriend Raffaele Sollectio was also convicted. Knox was sentenced to 26 years, and Sollectio was sentenced to 25 years.
Knox and Sollectio deny wrongdoing and have appealed the 2009 verdict.
In Italy, prosecutors also can appeal, and they did so in this case, using the appeals court to try for the harsher penalty.
Prosecutors are asking the appeals court for the same life sentence for Sollectio. They are also requesting six months of daytime solitary confinement for Knox and two months for Sollectio.
For two days, prosecutors sought to persuade the appeals court that there is sound evidence incriminating the defendants: witness testimony, genetic material, cell phone activity.
Manuela Comodi, summing up the case Saturday, said there is "gigantic, rock-solid circumstantial evidence." The prosecutors believe the defendants deserve the harshest possible punishment because of the brutal nature of the murder, the sexual assault, and the lack of a motive.
Kercher was stabbed to death in the apartment she shared with Knox, in what prosecutor said was a drug-fueled sexual aggression.
A verdict is expected in early October. A lawyer for the victim's family and the defense teams will deliver their closing arguments next week.
The Associated Press contributed to this report.