Clashes between troops and protesters killed six on May 15, bringing the toll from three days of violence to 24.
There have been running battles around the fortified camp where red-shirted protesters, who want the prime minister to resign, have been based since March.
In his first televised comments since the violence erupted on May 13, Mr Abhisit said he was trying to restore normality to the city with minimal losses.
He said a minority of red-shirts opposed to dialogue were putting the stability of the country at risk. "We will not retreat," he said.
Residents were being asked at security checkpoints to produce identification showing they lived in the area.
There were reports on May 15 that about 2,000 anti-government protesters had gathered on a main road near the camp.
More than 50 people have been killed and at least 1,500 wounded in total since the protests began in mid-March.
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