The body of 33-year-old Sarai Sierra, a mother of two, was found on Saturday near Istanbul's ancient city walls with fatal head wounds, the Radikal daily reported.
"We have confirmed that she was murdered by way of impacts on her head," Istanbul police chief Huseyin Capkin told reporters on Sunday. "But we need to conclude the investigation before details emerge."
The Milliyet newspaper said she was also stabbed several times in her abdomen, but there was no sign of rape or theft and she was still wearing jewellery when police found her.
Turkish police had been searching for Sierra after her family reported that they had lost touch with her on January 21, the day she was due to return home to New York.
The Hurriyet newspaper, along with other media outlets, reported that Istanbul police have arrested 11 suspects but gave no further details.
Sierra's body might have been dumped in a blanket on Tuesday night on the main road near the ancient walls, Hurriyet reported, citing a possible eye witness.
"I saw a man removing something from the back seat of a car," the woman was quoted as telling the police. "Then I saw a hand there."
Sierra, who has two children aged nine and 11, left the United States for Istanbul on January 7.
Sierra's body might have been dumped in a blanket on Tuesday night on the main road near the ancient walls, Hurriyet reported, citing a possible witness.
"I saw a man removing something from the back seat of a car," a woman was quoted as telling the police. "Then I saw a hand there."
Police had initially detained a Turkish man named Taylan K., who is believed to be the last person to see Sierra before she went missing, but released him after questioning, according to local reports.
The two had reportedly met online four months ago.
Hurriyet speculated that Sierra might have been tricked into trying to smuggle drugs into the United States, citing an anonymous retired US agent from the Drug Enforcement Administration.
But Capkin said there was no indication that she was involved in such a scheme. "She was a lonely wanderer," he said.
Istanbul is Turkey's largest city, home to at least 15 million people and considered a relatively safe travel destination which is visited by millions of tourists every year.