Deniz Baykal, head of the main opposition Republican People's party (CHP), and Zeki Sezer, his counterpart in the Democratic Left party (DSP), were due to attend Sunday's demonstration together.
"Whatever system the Turkish majority want should be done through elections"
Baz, Vancouver, Canada
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The choice of Samsun as the venue for the latest protest was symbolic.
It was in the Black Sea port city 88 years ago that Ataturk launched a liberation movement against the British, French, Italian and Greek troops occupying Turkey after the defeat of the Ottoman Empire in the first world war.
The rallies began last month after the AKP chose Abdullah Gul, the foreign minister, as its candidate for president.
The AKP failed to hold a parliamentary vote making Gul president, as a boycott by the opposition meant a quorum could not be attained.
The existing president is Ahmet Necdet Sezer.
The turmoil, exacerbated by a warning from the military that it stood ready to defend the secular order, forced Recep Tayyip Erdogan, the prime minister, to bring legislative elections forward to July 22 from November.
Opinion polls, however, suggest that the AKP is still Turkey's most popular party.
Despite its Islamist roots, the party has pledged commitment to secularism and carried out reforms that secured the opening of membership talks with the EU and stabilised the economy.
Opponents say the party still harbours Islamist ambitions, pointing at AKP policies such as opposition to a ban on the headscarf in universities and public offices, encouragement of religious schools and a failed attempt to restrict alcohol sales.