The protest began as a sit-in over plans to redevelop Gezi Park in Istanbul’s Taksim Square, but escalated after police used tear gas.
Tear gas was again fired on Saturday as hundreds of protesters marched over a Bosphorus bridge in Istanbul.
In Ankara, protesters tried to march on the parliament.
Hundreds of demonstrators marched over the bridge connecting the Asian and European shores of Istanbul on Saturday morning to try to reach the main square.
Police fired tear gas to try to disperse them and some protesters threw rocks. Police also fired tear gas in Taksim Square.
One Istanbul resident, who gave her name as Lily, told the BBC’s World Service: “There are 40,000 people crossing the bridge between Asia and Europe today. All the public transport is on lockdown.”
She said that police had dropped tear-gas canisters from helicopters overnight.
“About half past one the entire city started to reverberate. People were banging on pots, pans, blowing whistles,” she said.
The BBC’s Louise Greenwood in Istanbul says police from as far afield as Antalya are being drafted in to help quell the violence.
She says the central Taksim district and surrounding areas remain cordoned off and bridges are closed to traffic.
Istanbul’s governor said a dozen people were admitted to hospital and more than 60 people detained after Friday’s clashes.
In Ankara, protesters staged what they described as a solidarity rally, with many participants chanting: “Everywhere is resistance, everywhere is Taksim!”
On Saturday, protesters chanting anti-government slogans tried to march on the parliament.
The US has expressed concern over Turkey’s handling of the protests and Amnesty International condemned the police’s tactics.
Witnesses said tear gas was deployed randomly on people who were “by and large protesting peacefully”.
Demonstrators had gathered in Gezi Park on Friday to contest the controversial redevelopment project aimed at easing congestion around Taksim Square, which involved uprooting trees.
Opponents of Prime Minister Recep Tayyip Erdogan’s plans say the park is one of the few green areas left in central Istanbul.
Correspondents say the issue has helped highlight unhappiness among young people towards the government and ruling Justice and Development (AK) Party over what they see as creeping Islamisation.
Last week, Turkey’s parliament approved legislation restricting the sale and consumption of alcoholic drinks between 22:00 and 06:00.
The prime minister’s AK Party has its roots in political Islam, but he says he is committed to Turkey’s state secularism.
Mr Erdogan has been in power since 2002 and some in Turkey have complained that his government is becoming increasingly authoritarian.
Earlier this month, riot police clashed with tens of thousands of people attempting to hold a May Day march in Istanbul.
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