There have been daily street protests in anti-Erdogan neighbourhoods in Istanbul after Sunday's referendum, which the opposition claims was marred by blatant violations.
The Freedom and Solidarity Party (ODP), a left-wing movement not represented in parliament, said police had detained its Istanbul chairman Mesut Gecgel early today on accusations of "agitating the public" by claiming the 'Yes' vote was illegitimate.
Gecgel had himself written on Twitter that he was being detained for protesting against the 'Yes' victory.
Those detained are now reportedly being questioned at police headquarters in central Istanbul.
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There was no immediate confirmation of the detentions by the police.
Speaking in Ankara earlier today, Prime Minister Binali Yildirim said the issue of the election result was closed and warned against street protests.
"Turkey is a state of law... And there can be no talk of anarchy, activities in the street," he said.
"I call on people not to give in to provocations or get caught up in incitement," he added.
But the the main opposition Republican People's Party has formally requested that the Supreme Election Board (YSK) cancel the result due to alleged violations.
The opposition is particularly incensed by a last-minute move by the YSK to accept ballot documents in envelopes without an official stamp.