The protesters, who began their action over the weekend, want the government of PM Yingluck Shinawatra to step down.
After a huge rally on Sunday, crowds marched on Monday to several different locations in the city.
The protests have been triggered by a controversial political amnesty bill.
The legislation, which the opposition say would have allowed ousted leader Thaksin Shinawatra – the current prime minister’s brother – to return to Thailand without serving a jail sentence for corruption, failed to pass in the Senate earlier this month.
But the proposed legislation led to a fresh outbreak of street protests, reigniting simmering political divisions and raising the specter of renewed political turmoil in the South East Asian nation.
On Monday the anti-government protesters, who are led by a former opposition Democratic Party lawmaker, marched to state offices, military headquarters and television stations.
Campaign leader Suthep Thaugsuban had said the protest would be peaceful, with crowds “blowing whistles and handing out flowers”.
But at the finance ministry, a group of around 40 people swarmed into the compound.
“Tomorrow [Tuesday] we will seize all ministries to show to the Thaksin system that they have no legitimacy to run the country,” AFP news agency quoted Suthep Thaugsuban as saying.
Sunday’s demonstration drew an estimated 100,000 people, who called on the government to step down.
“We have stood by silently while her [PM Yingluck Shinawatra’s] brother calls the shots and she runs the country into the ground with loss-making policies,” Reuters news agency quoted protester Suwang Ruangchai, 54, as saying.
About 40,000 government supporters held a separate rally in another part of the capital on Sunday.
Thailand has been bitterly divided since Thaksin Shinawatra was ousted in a military coup in 2006.
Groups opposed to him occupied Bangkok’s main airport in 2008, shutting it down. Then in 2010, those who backed him and his allies held two months of street protests that paralyzed Bangkok.
Those demonstrations ended in a military crackdown. More than 90 people – mostly civilian protesters – died over the course of the two-month sit-in.
A government led by Thaksin Shinawatra’s sister was subsequently elected and since then Thailand has remained relatively politically stable.
But the opposition accuses Thaksin Shinawatra of running the government from self-imposed exile overseas, and the now-shelved amnesty bill has served as a spark for renewed protests.
The bill applied to offences committed during the upheaval after Thaksin Shinawatra was removed from office. Yingluck Shinawatra’s government had argued that the legislation was a necessary step towards reconciliation.
But critics said it would allow human rights abuses – such as the killing of civilian protesters – to go unpunished.
And the opposition viewed it as a way of overturning the jail sentence given to Thaksin Shinawatra, paving the way for his return.
Thaksin Shinawatra is a deeply polarizing figure in Thai politics. He drew huge support from Thailand’s rural poor but strong opposition from other sectors in society, and the divisions dating from the 2006 coup continue to dominate the political landscape.
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