RSF representative Erol Onderoglu, journalist Ahmet Nesin and rights activist and academic Sebnem Korur Fincanci were charged for taking part in a campaign of solidarity with a pro-Kurdish newspaper in May.
"The prosecutor in our case demanded that we be charged and jailed for terrorist propaganda", in support of the Kurdistan Workers' Party (PKK), an armed Kurdish rebel group that Turkish forces are battling in the country's southeast, Onderoglu told AFP by phone.
"This is another dark day for media freedom in Turkey," said Johann Bihr, the head of RSF's eastern Europe and central Asia desk, in a statement.
About 100 people rallied in support of the three outside the court in Istanbul where they made a brief appearance today. "We will not bow to pressure", the protesters chanted.
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The international community has voiced increasing alarm about the erosion of press freedoms in Turkey under President Recep Tayyip Erdogan.
"The authorities should drop the charges and stop using imprisonment as a way to fight differing voices," said Dunja Mijatovic, the OSCE media freedom representative, in a statement.
The arrests come despite the European Union pressuring Ankara to stop prosecuting academics and journalists and to change its terrorism laws, one of the conditions of its controversial migrant deal with Turkey that promises visa-free access for Turks, among other incentives.
Turkey is waging a large-scale military offensive against the PKK in the Kurdish-majority southeast, and has clamped down on those it accuses of supporting what it and its Western allies consider a terrorist group.