The Thai government says its priority now is to arrest the men it says fired on police during recent clashes with anti-government protesters. The government remains under pressure to call elections to ease political tensions.
Photos of men the government says fired on security forces have been splashed across newspapers and on television broadcasts.
Officials say men with military training, armed with semi-automatic guns and grenades, fired on troops as they clashed with anti-government protesters last Saturday.
Four soldiers, 16 protesters and a journalist died in the clashes, and more than 800 people were injured.
Spokesman Baranuj Smutharaks of the Democrat Party, which leads the governing coalition, says the priority is to address security threats, including scores of small bomb blasts in the capital.
"The government clearly laid out its plans to separate the use of the armed militia and the people responsible for that away from most of the people who have demonstrated," he said. "And I think the demonstrations require a political solution but the security threat and acts of terrorism require a security solution. The priority is addressing the security issues."
The bloodshed, after a month of anti-government protests in the city, has increased calls for Prime Minister Abhisit Vejjajiva to call elections.
Baranuj says polls could be held once tensions have eased. "Hopefully [elections can be held] when the country's ready and that people could go to the polls in peace. I think hopefully that will not be too long, but right now the major task is in restoring peace and bring the perpetrators before the law and reuniting the country," he said.
The protesters largely support former Prime Minister Thaksin Shinawatra, ousted in a 2006 coup. He now lives overseas to avoid prison for a corruption conviction.
Most are farmers or poor urban workers, who benefited from some of Mr. Thaksin's policies. But the rallies are attracting a wider middle class audience calling for greater income and power equality.
They want parliament to be dissolved immediately, but the government says it is better to wait six months to allow tensions to ease.
On Wednesday leaders of the protests moved all the demonstrators to location near large malls and hotels, abandoning the site where the rallies began in mid-March. Thailand is facing millions of dollars in lost revenue from a sharp fall in tourism and retails sales due to the protests.