Protesters cut off the electricity supply to the Thai national police headquarters on Thursday, in their latest bid to cripple government functions.
They also rejected a call by Prime Minister Yingluck Shinawatra to come to the table, which she made after shaking off attempts to dissolve Parliament.
"It is like a trap to get people to engage in an everlasting negotiation process so that they can keep their power," said movement spokesman Akanat Promphan.
Ms Yingluck made the appeal just hours after sailing through a no-confidence vote on the back of the ruling Puea Thai party's commanding majority in Parliament. The end of the two-day censure debate freed her to seek a fresh mandate through snap elections, but she did not take that option.
In a televised announcement, she rejected protesters' demands for a "people's assembly" that would work in tandem with the current legislative structure, saying it was not possible under the Constitution. But she urged protesters to go for talks.
"The political conflict has been prolonged and has done enough damage to the country," she said.
Street protests were sparked a month ago by the hasty passage of a Bill that would grant amnesty to former prime minister Thaksin Shinawatra, who was ousted in a 2006 coup and lives abroad to evade a jail sentence for corruption. Ms Yingluck is his sister.
Although the Puea Thai party later retreated on these plans, protesters now want to overthrow Ms Yingluck's government.
Nine lawmakers from the opposition Democrat party, including former deputy prime minister Suthep Thaugsuban, quit their posts in Parliament to concentrate on the protest.
Since Monday, thousands of protesters have surrounded ministries and government offices around Bangkok in a bid to cripple government functions and get civil servants to stop working for the "Thaksin regime". Last night, they were still camped out at the Finance Ministry and a key government complex.
The occupations have raised fears of renewed political unrest after two years of relative stability under Ms Yingluck's premiership. For several years after the 2006 coup, the kingdom was convulsed by tit-for-tat demonstrations by both sides of the political divide, one of which resulted in a military crackdown in 2010 that claimed more than 90 lives.
On Wednesday, United Nations Secretary-General Ban Ki Moon called on all sides to "exercise utmost restraint" and "resolve their differences through genuine dialogue and peaceful means".
Democrat party leader Abhisit Vejjajiva announced on Thursday his party shared the same goals as the protest movement, though he asserted it was run independently. The party said it would work with the protest movement as long as it is within the Constitution.
The party has tried to distance itself from some of the movement's more questionable tactics. The occupation of the Finance Ministry has already resulted in an arrest warrant for Mr Suthep.
"What Suthep is doing now is harming the Democrats in the long run," said commentator Verapat Pariyawong. Given that he was Mr Abhisit's deputy when the Democrat leader was prime minister from 2008 to 2011, Mr Suthep will always be associated with the party, he said.
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