The Saturday rally was organized by the National Solidarity Platform, an umbrella group of non-profit organizations, Hurriyet reported Sunday.
A representative for the group, Selda Talay Tosum, said their goal was a government based on the nationalistic ideals of the country's founder, Mustafa Kemal Ataturk, and not one based on Islamic principles, Hurriyet said.
Similar rallies were staged last year to protest the presidency of Abdullah Gul, who has strong links to political Islam.
Turkey's chief prosecutor, Abd a-Rahman Yalcınkaya, charged the ruling Justice and Development Party of Turkish Prime Minister Tayyip Erdogan with pushing an anti-secular agenda and moved to close it down.
The Constitutional Court in Turkey agreed to hear Yalcinkaya's case, although it could take several months.
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