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"But I don't think we owe an apology to those who have caused damage in the streets and tried to prevent people's freedom," he said.
Arinc said he would meet some of the organizers of the original Istanbul protest, which has spiraled into an unprecedented show of anger at the ruling party.
It appeared to be too little too late.
Shops were shuttered on a main avenue leading to Istanbul's Taksim Square, the focus of the protests, as thousands of demonstrators chanting anti-government slogans marched by. Barricades of rubble blocked other streets leading to the square and the acrid smell of tear gas hung in the air.
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A 22-year-old member of the main opposition youth wing was killed after being hit in the head at a rally in the southern town of Antakya near the Syrian border late on Monday, the second death after a taxi hit a demonstrator in Istanbul on Sunday. Officials initially said the Antakya victim had been shot.
The ferocity of the crackdown on the initial protests on Friday, which began over government plans to build over a Gezi Park in Taksim Square, shocked even Erdogan loyalists and drew international condemnation. U.S. Secretary of State John Kerry said he was concerned by reports of excessive police force.