Her defiance comes amid continuing violence in the Thai capital Monday that included an attempt by an angry mob to storm her office, the BBC reported.
Yingluck said she is open to talks with the protesters who say she and her government are being controlled by her brother, the exiled and disgraced former Prime Minister Thaksin Shinawatra.
Protesters, who have been on the streets since Nov. 24, want her replaced with a "people's council," the BBC said.
"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," Yingluck said in a televised address.
"The military has positioned itself as neutral and it wants to see a peaceful way out," she said.
"I believe that no one wants to see a repeat of history, where we saw the people suffer and lose their lives."
Yingluck ruled out early elections, telling the BBC that the country was not calm enough for polls.
Yingluck and her government were elected in national elections in 2011, but her administration has been dogged by accusations that she is a surrogate leader for her brother Thaksin. He was ousted in a bloodless military coup in 2006 that left the country divided.
Anti-government protests have been largely peaceful until deadly clashes with police on Sunday left three people dead in shootings between rival political camps, The New York Times reported.
Increased violence also led to more than 110 people being injured Sunday as about 30,000 people rallied in key locations around the capital. Protesters were met by riot police water cannons and tear gas, the Times reported.
Police also used rubber bullets, and many schools, universities and the main U.N. office have been closed for security, said Paradorn Pattanathabutr, head of Thailand's National Security Council.
The BBC reported military commanders have agreed to deploy troops to support the police on condition they wouldn't carry weapons and only would stand behind riot police ringing the main government offices.
Protest leader Suthep Thaugsuban, who met with Yingluck Sunday to deliver his resignation ultimatum, threatened to close down or occupy more government agencies and departments.
Suthep said the meeting at an undisclosed location was not to negotiate with Yingluck, but to spell out the demands of the protesters People's Democratic Reform Committee that wants a People's Council, The Bangkok Post reported.
"There was no negotiation and no compromise [with Yingluck]," he said. "This is the only one [meeting] and there will be no more until a victory for the people."
Yingluck's current round of troubles began in earnest last month after her government tried but failed to get an amnesty bill passed by both houses Parliament.
She publicly defended the controversial amnesty bill that would have allowed reconciliation for alleged political offenses during and after Thailand's 2006 coup.
The bill, which would have pardoned people, including political leaders, was passed unopposed by the lower House of Representatives but failed to pass the Senate last month, ending the bill's chances of becoming law.
The amnesty likely would have included Thaksin's sentence for corruption, the Post reported at the time.
Thaksin, who led the Pheu Thai party in government -- now his sister's party -- denied the allegations, but was sentenced in 2008 and soon after fled the country.
Yingluck continually denies that she takes orders from her self-exiled brother.
Notable deaths of 2014 [PHOTOS]