The authorities say they are targeting "terrorists" who have infiltrated the protesters' ranks, but TV footage has shown unarmed protesters being shot in the streets.
While the majority of the red-shirts are conducting their protest peacefully, some have been building barricades of tyres and setting them alight. Witnesses say others are armed with guns.
Late on Monday, the two sides held what is believed to be their first direct talks since the latest unrest broke out.
The government's chief negotiator Korbsak Sabhavasu said red-shirt leader Nattawut Saikuwa had called him and asked for a ceasefire.
But Mr Korbsak told the Associated Press news agency that nothing had been agreed.
On Monday, protests spread outside the capital with a military bus torched in Chiang Mai and demonstrations in two other northern towns.
Many of the protesters are from poor rural areas in the north, where support is still strong for former Prime Minister Thaksin Shinawatra, who was deposed in a 2006 coup.
The protesters say the current government is illegitimate, having come to power in a parliamentary vote after a pro-Thaksin government was forced to step down in December 2008 by a Constitutional Court ruling that it had committed electoral fraud.
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