Her skull had been fractured twice and she had been strangled with a cord or rope, Chief Prosecutor Giuseppe Creazzo said Thursday at a news conference, according to the Associated Press.

The prosecutor named Cheik Tidiane Diaw, 27, as the prime suspect, saying DNA samples from a condom and cigarette butt in the apartment matched his. Diaw was arrested on suspicion of aggravated homicide.

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"We have gathered serious indications of guilt against him," Creazzo said, according to the Associated Press.

The prosecutor said Olsen met Diaw at a local bar Jan. 8 and the two went back to her apartment. He said it appears the two — who had been consuming alcohol and possibly using drugs — had consensual sex.

"Then he probably slammed her head against something, twice fracturing skill, and then strangled her," Creazzo said, according to NBC News.

Investigators analyzed DNA from samples from the used condom and cigarette butt as well as from under Olsen's fingernails. Prosecutors said Diaw had also taken Olsen's cellphone, put his own SIM card in it and used it.

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On Friday, Olsen's parents, Paula and Walter Olsen, commended Italian authorities "for their swift apprehension of the perpetrator."

"Our deepest affections go to Ashley's many friends and to the community of San Frediano that she dearly loved," they said in a statement, according to the Associated Press.

Diaw's attorney, Antonio Voce, has since said that Diaw told investigators he and Olsen had consensual sex. Diaw also said that the two had been drinking and using cocaine, his lawyer told the Associated Press.

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But Diaw denied accusations that he strangled her.

During a police interrogation, Diaw told investigators that sometime after he and Olsen had sex, she tried to get him to leave her apartment because her boyfriend was due to arrive, his attorney told the Associated Press. Diaw said she pushed him against the door, and he punched her in the neck and then pushed her down. He said she hit her head on the ground.

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Diaw said he helped her to the bed and then left.

"He felt taken advantage of," Voce told the Associated Press. "She was still alive when he left."

Olsen moved to Italy nearly two years ago, announcing to friends on Facebook: "I got a one way ticket to Italy!” She studied fashion and soon found a home in Italy's art scene.

Her father is a professor at the Bianca Cappello Art Academy in Florence.

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Olsen's death has stirred up emotions in the country, recalling an incident in 2007 when a British student named Meredith Kercher was killed in what Italian police first called a sex game that had taken an ugly turn. It led to the contentious trial of her American roommate, Amanda Knox, and Knox's Italian boyfriend at the time, Raffaele Sollecito,

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“I would hope for [Olsen’s] sake that this investigation is more clear,” Georgette Jupe, a blogger who knew Olsen, told the Associated Press.

Creazzo, the prosecutor, said Thursday that authorities did not believe Olsen's death was a "sex game gone wrong," according to NBC News.

Olsen's death also comes during intense debate over the influx of migrants into Europe, one that intensified on New Year's Day when German police said many foreign men — including refugees — were suspected in a spate of sexual assaults in Cologne.

Creazzo said Diaw entered Italy illegally several months ago and had been making money handing out flyers for local bars and nightclubs.

Olsen's funeral is set for Friday afternoon at the Santo Spirito church in Florence.

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Olsen's family attorney said due to the ongoing investigation, her body cannot be returned to the United States. She will be buried in a cemetery in Florence.

"We are devastated that our precious Ashley has passed away resulting from a horrible and senseless crime," her father, Walter Olsen, said in a statement.

This story, originally published Jan. 14, has been updated.