In a 12-minute speech broadcast live on television, Ms Yingluck, also the defence minister, said there had been demands for her to resign, dissolve the House of Representatives, or to give power to an unelected council.
She was speaking from the Royal Thai Police headquarters on Monday afternoon.
Protest leader Suthep Thaugsuban, who on Nov 11 resigned as a Democrat Party MP for Surat Thani to lead an all-out protest against the Yingluck administration, met the prime minister on Sunday night. The meeting was held at the 4th Infantry Battalion, 1st Infantry Regiment on Vibhavadi Rangsit Road, and commanders of the three armed forces were also in attendance.
Mr Suthep, who faces a court warrant for his arrest, applied for by police, demanded on Sunday night that that Ms Yingluck "return power" to the people within two days, saying a "people's council" would be set up to pick a new premier to replace her.
He said that her resignation, or a snap general election, would not be enough.
"If there's anything I can do to bring peace back to the Thai people I am happy to do it," Ms Yingluck said.
"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 within the constitution.
"I don't know how we can proceed," with Mr 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."
People would not want to see a repeat of history, when people suffered and lost their lives, she said.
"If a House dissolution or my resignation can make the demonstrators return all the government offices and end their protests, I'm willing to do it," Ms Yingluck said.
When a reporter asked her about the army's position, she said the army has been neutral and wants to see peace in the country.
She urged all sides to jointly find means to end the ongoing political problem. The government is not attached to remain in power, she added.
Protesters on Monday centred their actions around Government House, the parliament and the Metropolitan Police Bureau in the historic quarter of the capital.
Anti-government protesters clash with police officers in different areas of Bangkok on Monday. (Bangkok Post photos)