BANGKOK, Thailand (CNN) -- Thai Prime Minister Yingluck Shinawatra dismissed calls by protesters for her to step down by Tuesday, saying she is open to talks to resolve demonstrations against her government that turned violent over the weekend.
Yingluck said in a televised news conference that it would be unconstitutional for her to step down and that the door was open for negotiations.
The leader of the anti-government demonstrations, Suthep Thaugsuban, on Sunday urged the democratically elected Yingluck to resign, saying he was giving her two days to "return power to the people unconditionally."
He made the comments after a face-to-face meeting with the Prime Minister in the presence of military leaders.
Suthep, a former deputy prime minister for the opposition Democrat Party, has called for power to be transferred to an unelected "people's council."
But Yingluck, who survived a no confidence vote in Parliament last week, is refusing to budge despite weeks of protests in the streets of the capital, Bangkok.
Monday evening, a Thai court issued an arrest warrant for Suthep on a charge of insurrection.
Worst unrest in years
On Saturday, three people were killed and more than 60 wounded in clashes between protesters and Yingluck's supporters -- the worst civil unrest in Thailand since a military crackdown on demonstrations in 2010.
On Sunday, police used tear gas to fend off demonstrators trying to force their way into the government headquarters. Many protestors had towels they soaked with water to hold over their mouths and eyes for the gas.
Yingluck reiterated Monday that authorities would not use violence against protesters, but police appeared to be resorting to increasingly tough measures to keep demonstrators at bay.
Lt. Gen. Paradon Patthanathabut said police at government headquarters had used rubber bullets in certain instances.
The number of protesters in the area appeared lower than in recent days, but hardcore elements seemed to be among those who remained. Tear gas canisters, rocks and bottles of water were hurled back and forth across the barricades.
The government headquarters, known as Government House, are a symbolic target for protesters. Amid the siege, Yingluck has decamped from the seat of government power to the police headquarters, said government spokesman Teerat Rattanasevi.
Demonstrators, meanwhile, continued to occupy official buildings they had stormed last week -- the Ministry of Finance and another complex of government offices.
But Suthep's call for a civil servants to go on strike appeared not to have taken hold Monday.
"Governmental agencies are all functioning normally," said Teerat. "But of course, some offices that have been taken over by these protesters have to work from their temporary setups."
Protesters say they want to rid Thailand of the influence of exiled former Prime Minister Thaksin Shinawatra, the older brother of Yingluck.
That's an ambitious goal in a country where parties affiliated with Thaksin, who built his political success on populist policies that appealed to Thailand's rural heartland, have won every election since 2001.
Thaksin was ousted in a military coup in 2006, and has spent most of the time since then in exile overseas. If he returns, he risks a two-year prison sentence on a corruption conviction, which he says was politically motivated.
The current protests in Bangkok were prompted by a botched attempt by Yingluck's government to pass an amnesty bill that would have opened the door for her brother's return.
That move added fuel for critics who accuse Yingluck of being nothing more than Thaksin's puppet, an allegation she has repeatedly denied.
The military -- which removed Thaksin amid protests in 2006 -- has remained on the sidelines of the current crisis. Yingluck said Monday that she believes the military is taking a neutral stance.
Chaos and commerce
Although the demonstrations have brought chaos to certain pockets of Bangkok and prompted warnings from foreign embassies to avoid protest areas, everyday life has continued in much of the city.
Some street traders have even adapted to service protesters needs.
On Sunday, many people down the street from the barricades near Government House, just out of reach of the tear gas, were cooking by the side of the road. Others were driving through with pick-up trucks giving food to protestors.
One enterprising vendor rode through the protest area selling ice creams in between volleys of tear gas.
CNN's Kocha Olarn and Paula Hancocks reported from Bangkok; Jethro Mullen reported and wrote from Hong Kong
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