Yingluck Shinawatra's comments, broadcast in a televised news conference, were the clearest indication yet that negotiations are unlikely to solve the country's increasingly violent political standoff.
As Yingluck spoke from the country's heavily fortified national police headquarters, stone-throwing protesters battled through clouds of police tear gas in a renewed attempt to seize her office, the Government House, and other key government buildings. As the day progressed, the protesters got hold of a garbage truck and a police truck, using them to break through parts of concrete barricades.
The protests aimed at toppling Yingluck's government have renewed fears of prolonged instability in one of Southeast Asia's biggest economies and comes just ahead of the peak holiday tourist season.
"If there's anything I can do to bring peace back to the Thai people I am happy to do it," Yingluck said, striking a conciliatory but firm tone. "The government is more than willing to have talks, but I myself cannot see a way out of this problem that is within the law and in the constitution."
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.
An anti-government protester carries a Thai national flag as he walk away from teargas during clashes with the police the metropolitan police headquarters in Bangkok. (Reuters photo)
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.
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.
The protesters' numbers have dwindled from a peak of 100,000-plus a week ago but a small groups of a few hundreds youths have remained at the frontline, fighting running battles with the police. They threw bottles, rocks and smoke bombs Monday over concrete and razor-wire barricades that they tried to rip down. They were repeatedly repelled by volleys of tear gas, bursts of water cannon and rubber bullets.
A monk puts on a gas mask as riot police use water cannon and tear gas while anti-government protesters attempt to remove barricades outside government house in Bangkok. (Reuters photo)
Many schools and offices, including the United Nations' regional headquarters located near the Government House, were closed.
The French Embassy issued one of the strongest warnings of dozens of foreign governments, urging citizens to "stay inside" to avoid the conflict on Bangkok's streets.
The French School was one of at least 60 schools closed in Bangkok on Monday. It is located in a northeastern Bangkok neighborhood where gunshots rang out over the weekend during clashes between Yingluck's supporters and opponents.
Suthep's meeting with Yingluck on Sunday took place in the presence of top military leaders, even though he has an arrest warrant against him. His sustained campaign has raised suggestions that he may have the backing of the military, which has long had a powerful influence over Thai politics. The army has often stepped in during times of crisis, carrying out 18 successful or attempted coups since the 1930s.
An anti-government protester walks past a police vehicle with the word 'police' painted into 'peace' outside the government house in Bangkok.(AFP photo)
Political instability has plagued Thailand since the military ousted Thaksin, who remains hugely popular among rural voters, in 2006.
Two years later, anti-Thaksin protesters occupied Bangkok's two airports for a week after taking over the prime minister's office for three months, and in 2010 pro-Thaksin protesters occupied downtown Bangkok for weeks in a standoff that ended with parts of the city in flames and more than 90 dead.
"I believe that no one wants to see a repeat of history, where we saw the people suffer and lose their lives," Yingluck said.