Turgeman, who chairs the Jerusalem Municipality's Planning and Construction Committee and has announced his decision to run for mayor, was arrested along with a relative of his.
Turgeman is suspected of receiving illicit benefits in exchange for promoting other people's interests. The Rishon LeZion Magistrates' Court extended his remand by three days.
Another suspect is a real estate entrepreneur who has held senior positions in the Israeli economy and was once nominated for the position of Finance Ministry director-general. He has been questioned in previous affairs as well.
Two of the other suspects are the owners of a banquet hall in Jerusalem.
Following the arrests, police conducted searches in the suspects' homes and offices.
The investigation is being conducted by the Israel Police and the Tax Authority and supervised by the Taxation and Economics Division at the Tel Aviv District Attorney's Office, focusing public corruption.
The Jerusalem Municipality has offered the following response: "The Jerusalem Municipality is unfamiliar with the details of the investigation, but will offer its full cooperation to the Israel Police and the law authorities in a bid to reach the truth and eradicate any possible public corruption in an uncompromising manner."
Eli Senyor, Yael Freidson and Roi Rubinstein.