ROME (CNN) -- American Amanda Knox vowed Tuesday to fight with her head "held high" to prove her innocence after Italian Supreme Court judges ruled Tuesday she should stand trial again for the death of her former roommate in Italy.

Knox spent four years in prison before an appellate court overturned her murder conviction, citing lack of evidence against her in the 2007 death of British student Meredith Kercher in Perugia.

Knox, who returned to the United States in 2011 and has been living in Seattle, was not in court for Tuesday's ruling.

The Supreme Court judges in Rome also ordered that her former boyfriend, Raffaele Sollecito, who was acquitted with her, face a new trial as well over Kercher's death.

Knox said it had been "painful" to hear the news that the court had ordered a retrial, in a statement issued through the family's PR spokesman, David Marriott.

The prosecution's case against her "has been repeatedly revealed to be completely unfounded and unfair," she said in the statement, and an "objective investigation" and "capable prosecution" are needed if any questions remain about her innocence.

"The prosecution responsible for the many discrepancies in their work must be made to answer for them, for Raffaele's sake, my sake, and most especially for the sake of Meredith's family. Our hearts go out to them," she said.

"No matter what happens, my family and I will face this continuing legal battle as we always have, confident in the truth and with our heads held high in the face of wrongful accusations and unreasonable adversity."

'Psychological impact'

Knox's attorney, Carlo Dalla Vedova, earlier told CNN that Knox was "upset and surprised because we thought that the case was over."

But, he added, "at the same time, as she's done in the last five years, she's ready to continue and we are ready to fight."

Dalla Vedova said he did not expect his client to leave Seattle for Italy "for many reasons," although she is free to travel.

"She's a very young girl and she's looking to have her life," he said. "This has a psychological impact on her."

Prosecutors have argued that despite the appellate decision, they still believe Knox and Sollecito are responsible for the death.

A lawyer for the Kercher family, Francesco Maresca, said the murdered girl's sister, Stephanie, said she was satisfied with Tuesday's ruling.

The Kercher family wanted a retrial because they believed the ruling that acquitted Knox and Sollecito was "superficial and unbalanced," he said.

The Kercher family believes more than one person was in the room when Meredith, 21, was killed, he said.

Another man, Ivorian drifter Rudy Guede, was convicted separately of Kercher's killing. Guede admitted having sexual relations with Kercher but denied killing her.

Judge Saverio Chieffi told the court he would publish the reasoning behind his decision within 90 days, after which the parties would have 45 days to present their case. The retrial is not expected until sometime early next year, to be heard in an appellate court in Florence.

After that, both parties would again be able to appeal at the Supreme Court.

Riccardo Montana, a law lecturer at City University London and an expert on the Italian legal system, said that the judges' decision to order a retrial is "not unusual when a case is very complex and there is a clear contrast between different accounts of the factual scenario."

While the Italian Supreme Court decides on points of law, the boundaries are not always clear, Montana said.

"In this specific trial, the use and interpretation of evidence was discussed," but the picture should become clearer when the full reasons for the court's ruling are issued in the coming weeks, he said.

Knox may be ordered to return to Italy for the retrial.

If she refuses, the Italian government could appeal to the U.S. government for her extradition.

But even if it does, Knox might still not end up before an Italian court.

Double jeopardy?

U.S. officials might reject such a request because it violates the U.S. legal principle that a criminal defendant can't be tried twice on the same allegation, said Joey Jackson, a contributor for HLN's "In Session."

Italy lacks the absolute prohibition present in U.S. law preventing authorities from retrying a criminal defendant who has been acquitted of a charge.

"We have principles that are well-founded within our Constitution, one of which is double jeopardy," Jackson said. "So as a result of that, I think it would be highly objectionable for the United States to surrender someone to another country for which justice has already been administered and meted out. So I don't think or anticipate that that would happen."

Another lawyer for Knox, Luciano Ghirga, said Monday that her client was confident in the Italian legal system and hoped one day to return to Italy as a free woman.

The Supreme Court did not order her retrial Tuesday on a charge of defamation.

Knox's conviction for defaming Patrick Lumumba, a club owner whom she accused of killing Kercher, was upheld in October 2011 by the same appeals court that cleared her of murder.

The case began in 2007, after Knox moved to Perugia to study at the University for Foreigners of Perugia for one year.

Knox, then 20, shared a room with British student Kercher.

That November, Kercher's semi-naked body was found at the home, with her throat slashed.

Police arrested Knox and Sollecito, who was her boyfriend at the time.

Two years later, they were convicted of murder, but they were cleared when they appealed the verdicts in 2011.

'Lack of evidence'

In legal paperwork published in December 2011, the judge in the case wrote that the jury had cleared the pair of murder for lack of evidence proving they were guilty.

Knox's family said last year the appeal was unwelcome, but no cause for concern.

"The appeal of Amanda's acquittal by the prosecution was not unexpected as they had indicated from the day of the verdict that they would appeal," a family statement in February 2012 said.

Knox has spent the last year and a half trying to resume a normal life, studying at the University of Washington in Seattle, her hometown.

She also has written a book on her ordeal, titled "Waiting to be Heard," which will be published next month.

According to Harper Collins, Knox "tells the full story of her harrowing ordeal in Italy -- a labyrinthine nightmare of crime and punishment, innocence and vindication -- and of the unwavering support of family and friends who tirelessly worked to help her win her freedom."

The publisher did not have any immediate response to the news that Knox now faces a retrial.

Francesco Sollecito, Raffaele's father, told CNN in a phone interview last year that the family was "not happy about the decision (to appeal). My son is trying to get back to normal life."

"We can do very little in this situation," he said, but as Italian citizens, they would have to accept the court's decision.

"We hope that the high court will finally put the words 'the end' to this story."

CNN's Ben Wedeman, Hada Messia and Livia Borghese reported from Rome, and Laura Smith-Spark wrote and reported in London. Karan Olson, Ed Payne and Michael Pearson contributed to this report.