The provincial governor of Burs, a northwestern province where Kurdish militant leader Abdullah Ocalan is imprisoned, had prevented a planned march which was declared illegal, and police had set up checkpoints on roads to Gemlik, a small port on the Marmara Sea across the water from the island prison where Ocalan is being held.
"We won't be able to hold the march today because of police obstruction," Aysel Tugluk, a Kurdish member of parliament, was quoted as saying by the state-run Anatolian news agency.
One convoy, of around 1,000 people, was stopped from leaving Diyarbakir, the main city in the mainly Kurdish southeast, on Saturday afternoon, NTV news channel reported.
Ocalan, head of the militant Kurdistan Workers' Party (PKK), is incarcerated on Imrali island south of Istanbul, and has held on-off talks with state officials seeking ways to end a separatist conflict that began in the 1980s.
The PKK is now fighting for greater autonomy and Kurdish rights, having earlier sought a separate state.
Ocalan's supporters want the state to recognise him as a legitimate representative of the Kurds in possible peace talks, and complain that he has been barred from seeing his lawyers for over two months.
More than 40,000 people have been killed in the conflict, including three victims of a car bomb in Ankara last month carried out by a PKK splinter group.
Turkey's military has been mounting air and artillery strikes since August on PKK positions in the Qandil mountains of northern Iraq, in reaction to a string of militant attacks.
Within Turkey, security forces have reportedly detained thousands of Kurds suspected of ties to the PKK in recent months. Interior Minister Idris Naim Sahin said on Friday that Kurdish media were exaggerating the numbers, though he said courts had formally arrested 277 suspects since Sept. 1.
On Friday night, according to Anatolian, police arrested 49 suspects in Istanbul and 18 in Diyarbakir.
They were picked up as part of an operation against a Kurdish organisation regarded as close to the PKK, which is listed as a terrorist organisation by Turkey, the United States and the European Union.