Officers fired tear gas and rubber bullets, leading many protesters to flee the square into adjoining Gezi Park, where many have been camping.
Some activists responded by hurling fireworks, fire bombs and stones at police.
Backed by armoured vehicles, 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.
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."
The demonstrations are now in their 12th day, with activists controlling much of Taksim Square.
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