The protests, the biggest in Turkey in recent years, were sparked by the police crackdown on Friday of a peaceful sit-in to prevent the demolition of a park in Istanbul.
Thousands later joined anti-government rallies across Turkey to voice discontent with the 10-year rule of Prime Minister Recep Tayyip Erdogan.
Turkey's state-run news agency said police have detained 25 people for "spreading untrue information" on social media and provoking protests.
The Anadolu Agency says Wednesday the people were detained in the city of Izmir for allegedly "inciting the people to enmity and hate." It said police were still looking for 13 others.
Turkey's main broadcast media have been criticized for shunning the coverage of police brutality at the protest onset on Friday. Many people turned to social media to keep up to date with the developments.
There were more clashes overnight, just hours after Turkey's Deputy Prime Minister Bulent Arinc offered an apology for violence at the hands of the security forces, CBC News correspondent Derek Stoffel reported from Istanbul.
"It seems it's now up to Arinc to try to defuse the situation here, as his boss, Prime Minister Regip Tayyip Erdogan is out of the country on a state visit," Stoffel said.
"Arinc was scheduled to meet later Wednesday with some of the protest organizers, but many of those camped out in central Istanbul say that's just a waste of time."
Many shops in the centre of Istanbul have been damaged or covered in graffiti by protesters.
Shop owner Altug Dortler, however, said he thought the protests were "very good for Turkish people and actually for the government also, because this is the first protest of the Republic of Turkey."
The protests are seen as a display of frustration with Erdogan, whom critics say has become increasingly authoritarian.
Many accuse him of forcing his conservative, religious Islamic outlook on the lives of secular Turks.
Union members gathered in Istanbul's Gezi Park on Wednesday, handing out fliers to passersby.
'Starting a war'
Arzu Cerkezoglu, president of the Confederation of Revolutionary Trade Unions of Turkey (DISK), said Erdogan and his government "should start caring about the wishes and demands of the people and the workers."
She accused the government of "starting a war" against the Turkish people.
"They banned the rights we won and deserve. They are selling the rivers, the mountains and have put all [Turkey's] assets on the open market," she said.
Under Erdogan's leadership, Turkey has boosted economic growth and raised its international profile.
But he has been a divisive figure at home, with his government recently passing legislation curbing the sale of alcohol and taking a strong stand against the Syrian regime that some believe has put security at risk.
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