Speaking on a discussion programme on broadcaster CNN Turk last week, Elci said "the PKK is not a terrorist group".
Police detained him in his office at around 2:20 am (2320 GMT) in Diyarbakir after an Istanbul court issued an arrest warrant. A crowd outside the office protested against his detention, video broadcast by CNN Turk showed.
The PKK, deemed a terrorist organisation by the United States and the EU, has been fighting an insurgency since 1984, demanding greater Kurdish autonomy in the southeast of the country. Some 40,000 people have been killed in the fighting.
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