The 24-year-old American sat motionless as Prosecutor Giancarlo Costagliola made his request. The prosecutor sought the same sentence for Knox's co-defendant, former boyfriend Raffaele Sollecito, capping two days of closing arguments by the prosecutors.
Costagliola also requested six months of daytime solitary confinement for Knox and two months for Sollecito.
A verdict is expected in early October.
Knox, of Seattle, Washington, and Sollecito, an Italian, were convicted by a lower court of sexually assaulting and murdering Meredith Kercher while they were all studying in Perugia in 2007. Knox was sentenced to 26 years, her co-defendant Raffaele Sollecito to 25 years.
They both deny wrongdoing and have appealed the 2009 verdict.
But in Italy prosecutors also can appeal, and they did so in this case. The prosecutors had sought life imprisonment, Italy's harshest punishment, in the original trial, too.
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.
"They have killed for nothing," she said.
Kercher was stabbed to death in the apartment she shared with Knox, in what prosecutor said was a drug-fueled sexual aggression.
Curt Knox, the defendant's father, said her daughter had reacted well to the prosecutors' request, which had been expected.
"She was actually fine. She said today was easier than yesterday, mainly because today was technical," he said. "Yesterday it was kind of character assassination that they tried."
Earlier Saturday, Comodi defended the forensic evidence that had been used to convict Knox, firing back at an independent review that criticized the investigation and the work of police in the case.
The DNA is crucial in the case, where no clear motive for the brutal killing has emerged.
Prosecutors maintain that Knox's DNA was found on the handle of a kitchen knife believed to be the murder weapon, and that Kercher's DNA was found on the blade. They said Sollecito's DNA was on the clasp of Kercher's bra as part of a mix of evidence that also included the victim's genetic profile.
But those findings were always disputed by the defense, and during the appeals trial the court decided to appoint two independent experts to review the evidence.
The independent experts challenged the prosecution's findings. They said police had made glaring errors in evidence-collecting and that below-standard testing and possible contamination raised doubts over the attribution of DNA traces, both on the blade and on the bra clasp, which was collected from the crime scene several weeks after the murder.
The review significantly weakened the prosecution case, giving Knox and her supporters hope that she might be freed after four years behind bars.
Sensing dangers, prosecutors have fought hard to try to undermine the review's results. They described it as superficial and sketchy. In several hearings in past weeks, and then again during summations Friday and Saturday, the prosecutors challenged the review point by point.
Comodi used down-to-earth expressions, simple language and even food analogies to keep the jurors engaged during the highly technical discussion about DNA testing and forensic science, which took about five hours. At one point, she pulled out a bra from her bag, seeking to illustrate how she thought the garment had been cut from the victim's body. She showed photos of bloody footprints found in the apartment, which she claims are compatible with the defendants.
Francesco Maresca, a lawyer for the Kercher family, supported the prosecution's stance on the review. Speaking after the court proceedings, he said: "They deserve the just penalty. Killing a girl - or anybody else - is punished by Italian law with life in prison, so they deserve life in prison, if they are found guilty."
Next week a lawyer for the victim's family and the defense teams will deliver their closing arguments.
"I think we'll have a little bit of a different story than what was portrayed in the last two days," said Knox's father.
Knox herself is expected to address the court before deliberations. The appeals trial, which opened in November, included several witnesses and a fierce debate over the DNA review, which was completed in June.
A third person, Rudy Hermann Guede of the Ivory Coast, also has been convicted of Kercher's murder in a separate proceeding. Italy's highest criminal court has upheld Guede's conviction and his 16-year prison sentence. Guede denies wrongdoing, but he admits he was in the house.