PERUGIA, Italy — An American student accused of murdering her British roommate in Italy had a growing hatred for the victim and killed her in retaliation during a drug-fueled sex game, a prosecutor said today in closing arguments at her murder trial.

Lead prosecutor Giuliano Mignini argued that Amanda Knox, together with her ex-boyfriend and co-defendant Raffaele Sollecito and a third man convicted in a separate trial last year, killed Meredith Kercher under “the fumes of drugs and possibly alcohol” and then tried to cover up their crime by staging a burglary.

Knox, of Seattle, wanted to get back at Kercher for saying she was not clean and for calling her promiscuous, Mignini said.

“Amanda had the chance to retaliate against a girl who was serious and quiet,” Mignini said. “She had harbored hatred for Meredith, and that was the time when it could explode. The time had come to take revenge on that smirky girl.”

He said Knox, Sollecito and Ivory Coast citizen Rudy Hermann Guede met at the apartment where Kercher was killed on Nov. 1, 2007, shortly before the slaying, likely to settle some drug issues with Guede, who was known in Perugia for dealing drugs. He said Kercher and Knox started arguing and then the three brutally attacked the Briton.

Kercher’s body was found in a pool of blood the next day, her throat slit.

Knox and Sollecito are charged with murder and sexual violence in the 2007 killing in the central Italian town of Perugia. They deny wrongdoing.

Guede was sentenced to 30 years in prison last year on the same charges. He also denies wrongdoing and is appealing his conviction.

Mignini recalled previous testimony by Kercher’s friends, in which the Briton expressed irritation at Knox’s behavior. Knox has denied having major problems with Kercher and has said in the past she was shocked at the death of a woman she considered a friend.

Mignini also said that Knox and Sollecito staged a burglary in the apartment by breaking a window in a bedroom in an attempt to sidetrack the investigation.

A rock was found in one of the bedrooms, and witnesses testified that shattered glass was found all over clothes on the floor, suggesting the window was broken after the room was put into disarray.

“The key to the mystery is in that room,” Mignini said. It would be nearly impossible to climb through the window without getting cut and leaving blood on the shattered glass.

Knox and Sollecito have been jailed for more than two years and appeared tense as they sat in court today.

Prosecutors were expected to formally make their sentencing requests to the eight-member jury Saturday, while a verdict is expected in early December.