“Government, resign!” protesters shouted as the police retreated.
The police is said to use excessive tear gas on protesters.
“We are here Tayyip, where are you?” they chanted, taunting Prime Minister Recep Tayyip Erdogan.
What began as an outcry against a local development project snowballed into a broader protest against what critics say is the government’s increasingly conservative and authoritarian agenda.
And since the first clashes on Friday, the unrest has spread to dozens of other cities across the country.
On Saturday, police in Ankara blocked a group of demonstrators from marching on parliament and the prime minister’s office.
Speaking at a rally on Saturday, Erdogan acknowledged: “It is true that there have been some mistakes, extremism in police response.”
But he added: “I call on the protesters to stop their demonstrations immediately.”
He also vowed to push forward with controversial plans to redevelop the square – the issue that sparked the protests.
The interior ministry promised legal action against police officers who had acted “disproportionately.”
The police have been heavily using tear gas on the protesters.
At Taksim Square, a popular tourist destination and traditional rallying site in Istanbul, the mood was defiant.
“We are still ruled by a prime minister who thinks people are lambs and declares himself the sultan,” said 19-year-old law student Batuhan Kantas, sitting exhausted on the ground.
Interior Minister Muammer Guler said that 53 citizens and 26 police officers had been injured across the country, with one person in intensive care at an Istanbul hospital.
The minister also said police had detained 939 protesters in more than 90 demonstrations in 48 cities, though some had later been released.
Officials said a dozen people were being treated in hospitals.
But Amnesty International spoke of reports of two deaths and more than a thousand injured, although there was no official confirmation of those figures.
In a statement, it said they opened its Istanbul offices, near Taksim Square, to give sanctuary to protesters and 20 doctors were treating injured protesters there.
Turkish protesters clash with riot police near the former Ottoman palace, Dolmabahce, where Turkey’s Prime Minister Recep Tayyip Erdogan maintains an office in Istanbul, Turkey, late Saturday, June 1, 2013. Turkish police retreated from a main Istanbul square Saturday, removing barricades and allowing in thousands of protesters in a move to calm tensions after furious anti-government protests turned the city center into a battlefield. A second day of national protests over a violent police raid of an anti-development sit-in in Taksim square has revealed the depths of anger against Prime Minister Recep Tayyip Erdogan, who many Turks view as increasingly authoritarian and dismissive of opposing views.(AP Photo)
Amnesty’s Europe director John Dalhuisen said police excesses in Turkey had become routine.
“But the excessively heavy-handed response to the entirely peaceful protests in Taksim has been truly disgraceful,” he added.
Human Rights Watch also suggested the real casualty figure was much higher than the official figures. One protester had lost an eye after police shot him with a plastic bullet, the group reported.
The US State Department called on Turkey to uphold “fundamental freedoms of expression, assembly and association, which is what it seems these individuals were doing”.
“We urge authorities in Turkey to exercise restraint and not to use tear gas indiscriminately,” the British foreign office tweeted on Saturday.
The Istanbul protest began as a peaceful sit-in at Gezi park across the iconic square.
The demonstrators had been preventing workers from razing some of the park’s 600 trees, the last patch of green in the commercial area, to make way for the restoration of Ottoman era military barracks. Residents fear that the barracks will be turned into a shopping mall.
But the demonstration soon took a violent turn after police fired rounds of tear gas to disperse the protesters.
Clashes raged overnight Friday to Saturday with thousands of people marching through the city, some banging pots and pans as residents shouted support from the windows.
Others held up cans of beer in defiance of a recent law by the ruling Justice and Development Party (AKP) that will restrict the sale and advertising of alcohol.
Erdogan’s populist government is regularly accused of trying to make the predominantly Muslim but staunchly secular country more conservative.
The location of the protests in Istanbul.
Edited for Telegraph.co.uk by Barney Henderson