During an interrogation by the police, he told them he had abandoned the woman's body, The Japan Times reported.
The torso was found on the ground and the arms covered with soil at the same location in Shimamoto.
Investigative sources say that on February 16th, the suspect and the woman were seen entering a building together in Higashinari Ward, Osaka, where he was staying.
A large amount of air freshener had been used in the condo and part of the woman's driver's license was found there also, the sources said. The family of a woman reportedly told police she was missing since her date with an American.
The New York man, who had been in Japan since January for sightseeing purposes, had first denied any allegations against him and refused to answer any questions authorities asked, according to the Asahi Shimbun. However, the woman was not found inside.
Both the NY man and the woman were spotted together on security footage at the JR Morinomiya Station in Osaka around midnight on Friday, Feb. 16, just hours before she went missing. Security cameras at the apartment where the suitcase was found show the missing Hyogo woman entering the apartment but she is never seen leaving, the Japan Time reports. It said he had been in contact with several women through dating apps, through which he met the 27-year-old woman.
Japanese media reported Bayraktar was from NY but didn't specify where.
The woman's head was found Saturday in a suitcase at a short-term lodging facility, or minpaku, in the Nishinari ward of the city of Osaka, investigators told the local news media.
Before she went missing, the woman had posted on Instagram that she was going to "meet Jay", an apparent reference to the American.
He had taken several other women to the same condominium, but police have confirmed that none of them have been harmed. A new warrant is to be served to the American man for disposing of and damaging a body.