The protests have brought clouds of teargas, rubber bullets and intermittent gunfire to parts of Bangkok, the latest turmoil in the struggle between the Bangkok-based establishment and forces loyal to Yingluck and her brother, former Prime Minister Thaksin Shinawatra.
Yingluck has promised not to use force against the crowds trying to storm her offices and the nearby metropolitan police headquarters which are protected by concrete barriers, razor wire and riot police.
Earlier on Tuesday, a helicopter dropped leaflets over the protesters reminding them that their leader, Suthep Thaugsuban, was wanted on a charge of insurrection.
"So please, stay away from him and stay away from the unlawful gatherings," media quoted the government as saying in the leaflets. Suthep, a former deputy prime minister bitterly opposed to Thaksin, vilified the police in a speech to his cheering supporters late on Monday and said the protesters would capture their city headquarters.
The fall of the police headquarters, or even the prime minister's offices in a complex known as Government House, to the protesters would not affect the legitimacy of Yingluck's government, which came to power after she won a landslide election victory in 2011.
But more chaos and violence would increase the chances of the army stepping in to restore order. Thai financial markets have fallen sharply since the protests began more than a month ago, but economic analysts say they do not expect a long-drawn crisis.
The violence has been restricted to a part of the capital, and economic activity is not affected in any way. On Tuesday, the baht was steady at around 32.15 to the US dollar, while the stock market closed 0.2 percent up on Monday.
Army neutral, so far
Thaksin was ousted in a 2006 coup and while Yingluck said on Monday the army was staying neutral, the generals might feel compelled to act in the event of a surge in violence.
Four people have been killed since the weekend and two protesters were shot and wounded on Monday, a hospital said, adding it was not known who shot them.
Thaksin's opponents hold considerable power and influence, among them wealthy conservatives, top generals, bureaucrats, royalists and many members of the urban middle class.
Many of them see Thaksin as a corrupt, crony capitalist who manipulates the masses with populist handouts and is a threat to the monarchy, which he denies.
He is adored by the urban and rural poor who would be outraged to see Yingluck's government removed. Yingluck said on Monday she was willing to explore every possibility for a peaceful solution. She could call an election, which her party would likely win.
Suthep, 64, who resigned as a Democrat lawmaker to lead the protests, wants a vaguely defined "people's council" to replace the government and a parliament made up of nominated worthies. Yingluck said that was unconstitutional.