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By Jacquellena Carrero, Praxilla Trabattoni and Claudio Lavanga

FLORENCE, Italy — The lawyer for the suspect in the murder of an American woman found strangled in Florence said his client fought with the woman, but left her alive and had no intention of killing her.

Senegalese migrant Cheik Tidiane Diaw was arrested in the murder of 35-year-old Ashley Olsen on Thursday morning after Olsen was found dead last week in her apartment in Florence.

Cheik Tidiane DiawItalian State Police

Diaw admitted under questioning that he had physically fought with Olsen after a night of drugs and sex but never meant to kill her, his attorney Antonio Voce told NBC News.

Diaw was arrested on suspicion of murder after his DNA was matched to a cigarette and a condom — his DNA was also found under Olsen’s fingernails, prosecutors said Thursday.

Florence Prosecutor Giuseppe Creazzo said at a press conference on Thursday that Olsen and Diaw met at a local bar called Montecarla late last Thursday or early Friday before they went to her home where evidence suggests they engaged in consensual sex.

At some point, their encounter turned violent.

An autopsy showed Olsen suffered two skull fractures and then was strangled with a rope or cord-like object, Creazzo said. The fractures alone could have killed her.

Ashley OlsenSara Tadros Snavely

According to The Associated Press, Olsen was found after her Italian boyfriend was worried that he hadn't heard from his girlfriend in a few days and asked the landlady to open the door. Her body was identified by her father, who also lives in Florence.

Attorney Anthony Voce said that his client had consensual sex with Olsen while the two were drunk and high on cocaine after they spent a night partying at the bar.

Diaw told investigators that he and Olsen argued when she tried to kick him out of her apartment after sex because she was afraid that her boyfriend would arrive, Voce told NBC News.

"She told him 'please go away,'" Voce said.

Olsen pushed Diaw to the door and when she turned her back to him, he punched the back of her head, Voce explained. They got into a shoving match and that’s when Voce believes she fractured her skull. Diaw denied that he strangled Olsen, telling investigators that he picked her up by the neck after she fell and put her on the bed.

According to Voce, when Diaw left Olsen’s apartment, she was alive and moaning that she was feeling unwell.

"He did not want to kill her or hurt her," the attorney said.

The Florence Prosecutor has said that police did not believe it was a "sex game gone wrong," a possible reference to the largely discredited Italian trial of American Amanda Knox in the city of Perugia in 2007. Italian police initially accused Knox and her boyfriend Raffaele Sollecito of killing her British roommate Meredith Kercher in a sex game gone wrong.

Olsen was originally from Summer Haven, Florida, but was living in the Oltrarno district of Florence and working in the fashion industry. She left the United States for Italy a few years ago to be close to her father, according to Italian news agency ANSA.

Her father, Walter Olsen, told NBC News in a statement on Wednesday that the family was devastated by the murder.

“She was a beautiful and creative young woman with a happy, exuberant and generous soul, and she loved her life in Florence, in San Frediano. We are heartbroken that she was taken from us,” the statement read.

The Associated Press reports that Olsen’s funeral is scheduled for Friday afternoon at the Santo Spirito church in Florence.