© Getty ImagesAnti-government protesters have been attacking barricades in an attempt to occupy Government House
Ms Yingluck said the demands were not possible under the constitution, but that she remained open to talks.
More clashes broke out on Monday as protesters tried to storm the prime minister's office, Government House.
Four people have died in Thailand's worst political turmoil since the 2010 rallies that ended in violence.
"Anything I can do to make people happy, I am willing to do... but as prime minister, what I can do must be under the constitution," Ms Yingluck said in a televised address.
Anti-government demonstrators have been calling on Ms Yingluck to step down, with protest leader and former opposition politician Suthep Thaugsuban saying on Sunday that Ms Yingluck should resign within the next "two days".
The protesters want to replace the government with an unelected "People's Council", alleging Ms Yingluck's government is controlled by her brother, ousted leader Thaksin Shinawatra.
The protests, which began on 24 November, had been largely peaceful until Saturday, when they became violent.
Over the weekend demonstrators tried to break apart police barricades and storm the prime minister's office, with police using tear gas and water cannons to repel them.
On Monday, protesters returned to the streets again and more clashes occurred, although correspondents said that demonstrator numbers appeared lower than before.
The mood of the protests appeared considerably nastier than over the weekend, with gangs of young men attempting to provoke riot police and smashing a police car, the BBC's Jonah Fisher in Bangkok reports.
Several schools and universities have closed, citing security concerns. AP news agency reported that 60 schools in Bangkok, as well as the main UN office, were shut.
The protesters had declared Sunday the decisive "V-Day" of what they termed a "people's coup". However, despite clashing with security forces, they failed to seize more government buildings or unseat Ms Yingluck.
Ms Yingluck has said that she would not authorise the use of force against protesters.
"The military has positioned itself as neutral and it wants to see a peaceful way out," she added in Monday's address.
Correspondents say that military commanders had agreed to deploy troops to support the police on condition they would carry no weapons and would stand behind riot police ringing the main government offices.
Ms Yingluck's brother, Mr Thaksin, was ousted in a military coup in 2006 that left the country bitterly divided.
Ms Yingluck's government, which has broad support outside the capital, took office after winning elections in 2011.
But the protesters allege that Mr Thaksin runs the government from overseas exile and accuse the current administration of using populist policies that are hurting Thailand's economy to remain in power.
On Friday Ms Yingluck ruled out early elections, telling the BBC that the country was not calm enough for polls.
Thailand is facing its largest protests since 2010, when thousands of red-shirt Thaksin supporters occupied key parts of the capital.
More than 90 people, mostly civilian protesters, died over the course of the two-month sit-in.
Reader Comments
to our Newsletter