Police briefly fired tear gas canisters and rubber bullets prompting many of the protesters to flee the square into Gezi Park, where scores had been camping.
But there were running battles at one edge of the square between police and some groups of protesters who fired fireworks, firebombs and stones at police water cannon.
Police made frequent announcements through loudspeakers, asking the group to stop attacking police and saying they did not want to use tear gas, before then firing the tear gas.
A water cannon could be seen dousing another police vehicle that was set alight by a firebomb.
The police clampdown on Taksim Square came on the 12th day of nationwide protests that were sparked by a violent police crackdown May 31 on a peaceful sit-in at a park in the square by people who were trying to prevent a redevelopment project that would replace the green space with a replica Ottoman Barracks.
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11 June 2013 Last updated at 10:34
The BBC's Mark Lowen:
"This is the biggest show of force in Taksim Square for well over a week"
Turkish riot police have moved into Istanbul's Taksim Square, which has been occupied by anti-government protesters for close to two weeks.
Officers fired tear gas and rubber bullets, leading many protesters to flee the square into adjoining Gezi Park. Some activists hurled fireworks, fire bombs and stones at police.
The unrest began after a crackdown on a protest over Gezi Park's redevelopment.
The Turkish prime minister said the move was hijacked to cause vandalism.
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At the scene
Mark LowenBBC News, Istanbul
Looking out at Taksim Square, I can see the clouds of tear gas that have covered the centre of Turkey's biggest city for much of the morning.
Police trucks have been spewing arcs of water cannon against the protesters, some of whom have responded with chunks of stone and petrol bombs.
The authorities claim this is an attempt to clear the square of banners, tents and flags scattered across it since the protest movement began 12 days ago. They say they will not enter the park that adjoins Taksim, the development of which first sparked the unrest.
The prime minister had called a meeting with protest leaders tomorrow. That announcement was seen as an olive branch - a potential diplomatic means to break the deadlock. But those talks may now be thrown into jeopardy by the strongest police action in Istanbul in over a week.
The original protests have widened, with demonstrators accusing Prime Minister Recep Tayyip Erdogan's government of becoming increasingly authoritarian and trying to impose conservative Islamic values on a secular state.
Mr Erdogan defended the police intervention on Tuesday.
In a speech in parliament that was frequently interrupted by applause, he asked: "What did the protesters expect? That we would kneel down before them?"
Backed by armoured vehicles and water cannon, officers wearing helmets and carrying shields gathered around the square early on Tuesday before moving past barricades erected by protesters.
They removed protesters' banners which had been hung from a building overlooking the square, replacing them with the national flag and a portrait of the father of the Turkish state, Kemal Ataturk.
Istanbul Governor Huseyin Avni Mutlu said the police had no intention of breaking up the protest in Gezi Park.
"Our aim is to remove the signs and pictures on Ataturk statue and the Ataturk Cultural Centre. We have no other aim," he wrote on Twitter. "Gezi Park and Taksim will not be touched."
A similar message was broadcast by police via loudspeaker, but protesters in the square said they did not believe this.
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The BBC's Mark Lowen, who is in the square, says this was a deliberate show of force that may jeopardise plans by Mr Erdogan to meet the protest organisers on Wednesday.
Three people have died and more than 5,000 have been injured since the protests began.
Smaller protests have occurred in the capital Ankara too. Police there have used water cannon and tear gas to break up demonstrations almost every night.