Suthep Thaugsuban, who resigned as an opposition Democrat Party lawmaker to lead the protests, has insisted he will not negotiate.
The demonstrators, most of them sympathetic to the Democrat Party, have taken over or surrounded several ministry buildings, which Yingluck said failed to shut down the government but created the potential for violence.
Police spokesman Piya Uthayo said a total of about 15,000 protesters were grouped Thursday at about six locations in and around Bangkok.
Yingluck has been reluctant to use force to evict the protesters for fear of escalating the conflict and sparking bloodshed, which would harm investor confidence and the lucrative tourism industry.
"The fact that the government has followed peaceful means does not mean the government cannot administer the country or cannot enforce the law to provide order," she said in a televised speech.
Hordes of demonstrators marched to the police headquarters in the center of Bangkok where they cut the electrical lines to the compound. Helmeted riot police with shields remained holed up inside, but did nothing to stop them.
The police headquarters is just down the street from the site of pro-Thaksin demonstrations in 2010 that tied up business in central Bangkok for two months. Violence, capped by a military crackdown, left more than 90 people dead.
The crackdown was ordered by Suthep, who was deputy prime minister of the Democrat Party-led government at that time.
On Sunday, more than 100,000 people rallied in Bangkok against Yingluck's government.
Suthep says his goal is to replace the government with a non-elected council an apparent call for less democracy, not more. He says the change is necessary to uproot the Shinawatra political machine from Thai politics. Thaksin remains highly popular in rural areas, and parties allied with him have won every election since 2001.
Yingluck responded that a change to a non-elected council is impossible under the constitution.
Thaksin, who lives in Dubai to avoid a two-year jail term for a corruption conviction he says was politically motivated, is a highly polarizing figure in Thailand. An ill-advised bid by Yingluck's ruling Pheu Thai party to push an amnesty law through Parliament that would have allowed his return sparked the latest wave of protests earlier this month.
Thaksin won over much of Thailand's rural underclass while prime minister by introducing populist policies designed to benefit the poor. His political movement became the most successful in modern Thai history.
But his opponents, largely members of the urban middle class and elite, see him as a threat to democracy and their own privileges, and have fought back hard. After the 2006 coup that ousted Thaksin, a new constitution was drafted to reduce his influence. Controversial judicial rulings removed two pro-Thaksin prime ministers, and army-backed parliamentary maneuvering allowed the Democrat Party to form a government.
Since taking office with a landslide electoral victory, Yingluck has managed a fragile detente with the military that toppled her brother, and faced major crises including floods that ravaged the country in 2011, the worst in half a century.
