The naked body of Ashley Olsen was found last week in her flat, shocking friends and the local community who described her as "kind" and "gentle".
More lab results are needed to determine the time of the 35-year-old's death, prosecutors said.
When she was found, she had bruises and scratches on her neck.
Her Italian boyfriend said he had not heard from her and he later found her in her apartment.
Olsen was from Summer Haven, Florida, and had been living in Florence for three years.
"While we mourn her passing we place our trust fully in the Italian authorities to investigate this tragic episode,'' Olsen's friends wrote in English-language newspaper The Florentine, calling her death "horrific" and "unimaginable".
"We wait to hear what they discover, and pray that justice will be swiftly served to whoever his responsible."
Italian police hope DNA traces collected in the apartment will help find the killer.
One line of enquiry could be that she met up with a man the night of her death.
Witnesses and CCTV footage show her meeting up with a man after leaving the nightclub where she was last seen, Agence France-Presse reports.
Prosecutors have not said whether drugs were found in the apartment.
An American woman living in Florence was strangled to death with an object like a rope or cord, an Italian prosecutor has said.