The protesters sought resignation of the government of Prime Minister Yingluck Shinawatra, saying it was controlled by her brother Thaksin Sinawatra, the ouster former prime minister of the south-east Asian nation.
The protesters marched towards several locations in the national capital following a huge rally held on Sunday.
Prime Minister Shinawatra invoked special powers for officials to impose curfews but said on Tuesday that authorities would not resort to violence to deal with the protesters. She hoped that talking to the protesters could be a way out of the mess.
Meanwhile, the country's criminal court issued an arrest warrant for Suthep Thaugsuben, the former opposition Democratic Party legislator, who led the protests that were fuelled by a controversial political amnesty bill which the protesters believed whould allow the former prime minister to return to Thailand without serving the jail sentence he was awarded in 2008 after being convicted in absentia of corruption.
Thailand has been witnessing a rough time since Thaksin Shinawatra was ousted in a military coup in 2006.