Between 100,000 and 150,000 demonstrators rallied in Bangkok, with protest leaders saying their goal Monday is to storm Shinawatra's office, known as Government House.
The country will hold new elections by February 2, but embattled Prime Minister Yingluck Shinawatra may not be her party's choice to run, a government spokesman told CNN on Monday.
"I don't know whether the Pheu Thai Party will still vote (for) her to run again or not," said spokesman Teerat Ratanasevi, referring to the ruling party.
Yingluck's move Monday comes a day after Thailand's main opposition party, Democrat Party, said its roughly 150 members would resign en masse from parliament because they could no longer work with the government.
"I don't want our country and the Thai people to suffer from more losses," Yingluck said in a televised address.
But opposition party leader Abhisit Vejjajiva said the massive protests leave the government little choice.
"I think the best way for the Prime Minister to show responsibility is by returning power to the people," he told CNN.
Still, dissolving parliament and calling elections appear unlikely to placate protest leader Suthep Thaugsuban, a former deputy prime minister for the Democrat Party. He has called for power to be transferred to an unelected "people's council."
Thaksin's influence
During the weeks of demonstrations, protesters have occupied various government offices. The rallies have been mostly peaceful, but clashes between protesters and government supporters on November 30 left five people dead.
Protesters and police, who had confronted each other with tear gas and rocks in parts of Bangkok last week, agreed to a truce Tuesday in a show of respect for Thailand's revered king, who celebrated his 86th birthday Thursday.
Protest leaders have said they want to rid Thailand of the influence of former Prime Minister Thaksin Shinawatra, the older brother of Yingluck.
That's an ambitious goal in a country where parties affiliated with Thaksin, who built his political success on populist policies that appealed to Thailand's rural heartland, have won every election since 2001.
Thaksin was ousted in a military coup in 2006 and has spent most of the time since then in exile overseas. If he returns, he risks a two-year prison sentence on a corruption conviction, which he says was politically motivated.
The current protests in Bangkok were prompted by a botched attempt by Yingluck's government to pass an amnesty bill that would have opened the door for her brother's return.
That move added fuel for critics who accuse Yingluck of being nothing more than Thaksin's puppet, an allegation she has repeatedly denied.