Police firing tear gas cleared the square on Tuesday morning, but protesters returned later in the day.
Istanbul’s governor, Huseyin Avni Mutlu, said operations would go on night and day to clear the square.
Protests began 12 days ago over the redevelopment of nearby Gezi Park.
The protests then widened, with demonstrators accusing Recep Tayyip Erdogan’s government of becoming increasingly authoritarian and trying to impose conservative Islamic values on a secular state.
On Tuesday evening, protesters in Taksim Square lit bonfires, set off fireworks and threw stones at police.
Officers responded by firing tear gas, but crowds still remain in the square.
“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,” Huseyin Avni Mutlu said in televised comments.
But he also said the action would “be conducted with care, in front of our people’s eyes, in front of televisions and under the eyes of social media, with caution and in accordance with the law”.
Recep Tayyip Erdogan defended the police intervention on Tuesday, saying that an environmental movement had been hijacked by people who wanted to harm Turkey.
In a televised speech to members of parliament belonging to his Justice and Development Party (AKP) that was frequently interrupted by applause, he asked: “They say the prime minister is rough. So what was going to happen? Were we going to kneel down in front of these [people]?
“If you call this roughness, I’m sorry, but this Tayyip Erdogan won’t change.”
“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.”
Early in the day, police made loudspeaker announcements, telling protesters to withdraw from the square, before using water cannon, tear gas and rubber bullets to clear them.
Bulldozers were sent in to clear barricades and shelters.
They also removed protesters’ banners from a building overlooking the square, replacing them with the national flag and a portrait of the father of the Turkish state, Kemal Ataturk – who has also been used as a symbol by demonstrators.
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 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.
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