Taksim Square, the focus of days of protest, is now largely cleared, BBC reported.
But protesters have regrouped in nearby Gezi Park, whose proposed redevelopment sparked anger which has widened into nationwide anti-government unrest.
Prime Minister Recep Tayyip Erdogan has said there will be no tolerance of people he accuses of seeking to harm Turkey.
The demonstrators accuse Erdogan of becoming increasingly authoritarian.
Erdogan is due to meet a group of people - including an actress, a singer and a writer - who he hopes can mediate with the protesters.
It had been suggested he would hold talks with protest organizers, but they said that they had not been approached by the prime minister - and would refuse to meet him even if they were.
They added that they did not recognize any of the group that Erdogan was due to meet as representatives of the protesters in the park.
Throughout Tuesday, riot police had repeatedly clashed with protesters throwing bottles, stones and firebombs. Many peaceful demonstrators were also caught in the clashes.
Thousands converged on the square as night fell and were repelled by water cannon, rubber bullets and tear gas.
Dispersed demonstrators sought shelter nearby, including in Gezi Park. Police said they did not plan to enter the park.
Volunteers set up makeshift clinics to treat anyone injured.
Security forces cleared the square, only for the demonstrators to return.
Istanbul Governor Huseyin Avni Mutlu had earlier struck a conciliatory note, but he went on television on Tuesday night to declare, "We will continue our measures in an unremitting manner, whether day or night, until marginal elements are cleared and the square is open to the people. "
Erdogan has defended the police action, saying that an environmental movement against the demolition of the park had been hijacked.
In a televised speech, he said, "To those who... are at Taksim and elsewhere taking part in the demonstrations with sincere feelings: I call on you to leave those places and to end these incidents and I send you my love.
"But for those who want to continue with the incidents I say: 'It's over.'
"As of now we have no tolerance for them. "
The protests began on 31 May.
The Turkish Human Rights Foundation says four people have been killed, including one policeman.
Some 5,000 protesters have been treated for injuries or the effects of tear gas, while officials say 600 police officers have also been injured.
Protests have also occurred in the capital, Ankara, with smaller demonstrations in many other cities.
Police in Ankara have used water cannon and tear gas to break up demonstrations almost every night.
German Foreign Minister Guido Westerwelle said that the Turkish government was sending the wrong signals at home and abroad with its reaction to the protests, describing the pictures from Taksim Square as disturbing.
"We expect Prime Minister Erdogan to de-escalate the situation, in the spirit of European values, and to seek a constructive exchange and peaceful dialogue," he said in a statement.
Meanwhile, Turkey's broadcasting regulator has fined four small Turkish TV channels over their coverage of anti-government protests, accusing them of "encouraging violence".