Hundreds of officers have been using tear gas and water cannon to disperse activists.
The move comes after PM Recep Tayyip Erdogan agreed to meet the protest organizers on Wednesday.
The unrest was sparked by a police crackdown on a local protest over an Istanbul 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.
Backed by armored vehicles, police wearing helmets and carrying shields gathered around the square early on Tuesday.
They then began to move past barricades erected by protesters.
According to correspondents, the move is a deliberate show of force.
The demonstrations are now in their 12th day, with activists controlling much of Taksim Square.
The unrest was sparked after police moved to suppress environmental protests over the redevelopment of Gezi Park, which is part of Taksim Square, on May 31.
More than 5,000 people have been injured and three people have died since the protests began.
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