RSF Turkey representative and journalist Erol Onderoglu, journalist Ahmet Nesin and rights activist and academic Sebnem Korur Fincanci were charged on Monday in connection with "terror propaganda" after guest-editing the pro-Kurdish Turkish daily Ozgur Gundem.
The three have been remanded in custody and are being held in Metris prison in Istanbul. Prosecutors have demanded they be given jail terms of up to fourteen-and-a-half years.
"The request lodged on Thursday for their liberty has been rejected," RSF secretary general Christophe Deloire told AFP.
On Friday, Deloire led a protest outside the gates of the Istanbul jail with demonstrators holding pictures calling for the trio to be released.
Also Read
The case has stoked concerns over the state of basic freedoms in Turkey, with the United States expressing deep concern over "a troubling trend that we've seen in Turkey to discourage legitimate discourse and freedom of expression, freedom of the press."
In a statement released earlier this week, the watchdog said arrests marked a new stage in Turkey's crackdown on activists fighting for human rights.