Italy's highest appeal court has ordered a fresh trial in the case of the murder of British student Meredith Kercher, overturning the acquittals of Amanda Knox and Raffaele Sollecito and paving the way for a potential extradition tussle between Italy and the US.

In a ruling, which came more than five years after the 21-year-old from Surrey was found dead in the university town of Perugia, the court of cassation quashed the acquittals handed down by an appeals court in 2011. Its decision was not based on the presumed guilt or innocence of Knox or Sollecito, but was intended to hinge solely on whether or not the appellate trial had been properly conducted.

The new trial, which will be held at Florence's court of appeal, will be a repeat of the appeal trial held in Perugia in 2011.

The move came after prosecutors had argued that the court that acquitted Knox, 25, and Sollecito, who turns 29 on Tuesday, had "lost its bearings" in the case and had erred in numerous ways, including insufficient forensic evidence tests.

The court had heard six hours of arguments from both prosecutors arguing for the case to be reopened and their defence lawyers insisting the pair had been rightly cleared two years ago.

Neither Knox nor Sollecito was in court to watch the proceedings. The Kercher family did not attend, but Sollecito's father, Francesco, was present on Monday.

Within minutes of the ruling, Knox issued a statement condemning the arguments on which it appeared to be based as "unfounded and unfair".

Raffaele Sollecito, Knox and Rudy Guede. Photographs: AP and EPA

"It was painful to receive the news that the Italian supreme court decided to send my case back for revision when the prosecution's theory of my involvement in Meredith's murder has been repeatedly revealed to be completely unfounded and unfair," Knox added.

"I believe that any questions as to my innocence must be examined by an objective investigation and a capable prosecution. 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. 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."

Knox breaks down after hearing that she had been acquitted in 2011, after serving four years in prison. Photograph: Pier Paolo Cito/AFP/Getty Images

Franceso Maresca, the Kercher family lawyer, said he had spoken to Stephanie Kercher, Meredith's older sister, who he said was "very happy and satisfied" with the ruling. The family would continue to try to "get to the bottom" of the case, he added.

The ruling by the panel of five judges paves the way for future friction between Italy and US over Knox's fate. Since returning to her home city of Seattle in autumn 2011, she has enrolled at the University of Washington, found a new boyfriend and written her memoirs, clinched in a deal reportedly worth $4m.

Although she will not have to be present for the Florence retrial, her lawyer, Carlo Dalla Vedova, said Italy could request her extradition if she were convicted a second time. It would then be up to the US to decide whether to agree to the move, something some observers say is unlikely.

Giulia Bongiorno, defence lawyer for Sollecito, told Italian television channel Sky TG24: "As today is his birthday I would have liked to tell him that this affair was over … and to give him this joy. Quashing an acquittal does not imply a belief that the accused are guilty but indicates a desire by the judges of the court of cassation to request further analysis."

Meredith Kercher's mother Arline, brother Lyle and sister Stephanie at a press conference in Perugia, Italy. Photograph: Franco Origlia/Getty Images

Kercher, a University of Leeds student on a year abroad in the historic town of Perugia, was found dead in a pool of blood in her bedroom on 2 November 2007, partially clothed and with her throat slashed.

In October 2008, Rudy Guede, from the Ivory Coast, was found guilty of sexually assaulting and murdering Kercher, and is serving a reduced sentence of 16 years in prison.

In December 2009, after a separate trial, Knox and Sollecito were also convicted of the killing and were sentenced to 26 and 25 years in jail respectively.

After four years in prison, the pair were acquitted in a dramatic ruling in October 2011. The court found that DNA evidence used to convict them had been unreliable. Four months later, prosecutors lodged an appeal in which they claimed the verdict contained numerous omissions.