Protest leader Suthep Thaugsuban, who met with Yingluck on Sunday night, has said he will not be satisfied with Yingluck's resignation or new elections.
Instead, he wants an unelected “people's council” to pick a new prime minister who would replace Yingluck, even though she was elected with an overwhelming majority.
His demand has been criticized by many as undemocratic.
“I don't know how we can proceed” with Suthep's demand, she said.
“We don't know how to make it happen. Right now we don't see any way to resolve the problem under the constitution,” she said in the brief 12-minute news conference.
She cited Suthep's repeated statements that he won't be satisfied even if she steps down to end the deadlock, and implied that she was willing to hold fresh elections if that helps.
“I am not against either resignation or dissolution of parliament if this solution will stop the protests,” she said. “The government is not trying to cling to power.”
The protesters, who are mostly middle-class Bangkok supporters of the opposition Democrat Party, accuse Yingluck of being a proxy for her brother, former Prime Minister Thaksin Shinawatra.
He was deposed in a 2006 military coup but remains central to Thailand's political crisis, and is a focal point for the protester's hatred.
The protesters, who call themselves the People's Democratic Reform Committee, say their goal is to uproot the political machine of Thaksin, who is accused of widespread corruption and abuse of power.
Monday's violence took place around key institutions—the Government House, the Parliament and Metropolitan Police Headquarters in the historic quarter of the capital.
The area has some of Bangkok's main tourist attractions such as the Grand Palace, Wat Pho temple, the Bangkok zoo, and the backpacker area of Khao San Road. Most of Bangkok, a city of 10 million, has been unaffected.
Analyst Thitinan Pongsudhirak told The Associated Press that while Suthep's demands may appear “bold and blatant,” they go down well with the people ... who think that the electoral system can never be trusted and therefore they have to set up their own government and rewrite the rules.”
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