They also are demanding that Prime Minister Recep Tayyip Erdogan resign, accusing him of imposing his conservative Islamist views on a secular nation.
The prime minister plans to meet with some of the demonstrators Wednesday, but accuses them of deliberately trying to damage Turkey’s image and economy.
He says the protesters are “trying to prevent turkey’s rise and are being used by financial institutions and media groups to harm Turkey’s economy.
Three people have died since the protests began almost two weeks ago. About 5,000 people have been hurt and thousands of others arrested.
Police also fired fired water cannons Tuesday to disperse protesters in Ankara, the capital, who had gathered in sympathy with their Istanbul counterparts.