The protesters want Yingluck Shinawatra’s government to resign, saying it is controlled by her brother – ousted former PM Thaksin Shinawatra.
After a huge rally on Sunday, they marched to several Bangkok locations.
Late on Monday, Yingluck Shinawatra invoked special powers allowing officials to impose curfews and seal roads.
The protests have been triggered by a controversial political amnesty bill.
The demonstrators say the legislation – which failed in the Senate – would have allowed Thaksin Shinawatra to return to Thailand without serving a jail sentence for corruption.
Thailand has been bitterly divided since Thaksin Shinawatra was ousted in a military coup in 2006 and the proposal re-ignited simmering political tensions.
Groups of protesters, who are being led by former opposition Democratic Party lawmaker Suthep Thaugsuban, camped out at the foreign and finance ministries overnight.
On Tuesday, they surrounded the interior, tourism, transport and agriculture ministries.
There were around 1,000 protesters gathered outside both the finance and interior ministries, blowing whistles and chanting “get out!”, reports said.
“We have to leave because they [the protesters] will cut the utilities,” Tourism and Sports Minister Somsak Pureesrisak told AFP news agency.
Akanat Promphan, a protest spokesman, said: “We are occupying the finance ministry in a non-violent and peaceful way, so our supporters around the country can do the same and occupy all government offices.”
“Tomorrow there will be a nationwide movement,” he added.
However, Thida Thavornseth, a leader of the “red shirts”, who support Thaksin Shinawatra, told AFP news agency: “Suthep [Thaugsuban] is not trying to throw out the government… he wants to throw out democracy and replace it with an ultra-royalist administration.”
The opposition Democrat Party has also started a censure motion in parliament against the government, over its alleged misuse of the budget.
The motion highlights an expensive rice subsidy scheme launched by the government after it took office.
Under the scheme, the government bought rice directly from farmers, paying more than the market rate. India and Vietnam increased their share of global rice exports as a result, overtaking Thailand as the world’s largest rice exporter.
The government is expected to defeat the censure motion, since the ruling Pheu Thai party has a majority in parliament.
The protests are the biggest to hit Thailand since the violence of 2010, when “red-shirt” opponents of the then Democratic Party government occupied key parts of the capital.
More than 90 people, mostly civilian protesters, died over the course of the two-month sit-in.
A government led by Yingluck Shinawatra and the ruling Pheu Thai Party 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.
Yingluck Shinawatra invoked the Internal Security Act late on Monday. But she said on Tuesday the government would not use violence to end the protests.
“Everybody must obey the law and not use mob rule to upstage the rule of law,” she told reporters.
“If we can talk, I believe the country will return to normal,” she added.
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