The decision came hours after a defiant Prime Minister Samak Sundaravej went on national radio and vowed he would not step down.
His combative speech intensified the deadlock with the People's Alliance for Democracy, whose supporters in their thousands have taken over the sprawling lawns of Samak's office compound since storming through the gates on Aug. 26.
Describing the alliance as an anti-democractic group and their actions as a shameful embarrassment for the country, Samak said he will not bow to its demands.
"I will not abandon the ship, and I will take responsibility for the crew on board," Samak said, peppering his speech with folksy language. "I am not resigning. I have to protect the democracy of this country."
A referendum could show a way out of the deadlock.
Culture Minister Somsak Kietsuranond told reporters that no date has been set for the referendum and the exact topic also remains unclear.
But the possible questions that would be asked include whether the government should resign, whether it should dissolve Parliament and what people think about the ongoing protest, he said.
"The Cabinet just agreed in principle for now," he said, referring to the fact that there is currently no law providing for referendums.
"Whether it can be done and when it can be done depends on when the organic law on public referendums is passed by the Senate," said deputy government spokesman Nattawut Sai-gua.
The announcement was met with skepticism from the anti-government protesters camped in the compound of Samak's office, Government House.
"This is just a political game the government is trying to play. The government is not fixing the problems the PAD is talking about. This protest is about making sure the government corrects its mistakes," said Pichet Pattanachote, a former vice president of the Senate who has joined the alliance.
The protesters are living under makeshift tents, and organizers have set up a high stage from which leaders deliver regular speeches between music concerts that keep the protesters entertained.
The alliance has already helped force one prime minister from power - staging demonstrations in 2006 that paved the way for the bloodless military coup that removed Thaksin Shinawatra.
Thaksin, a telecommunications tycoon, recently fled to Britain to escape corruption charges. The protesters say Samak is Thaksin's stooge and is running the government for him by proxy. They accuse Samak's government of corruption and making unconstitutional decisions.
Bloody rioting between supporters of Samak and the alliance left one person dead and dozens injured early Tuesday, the only violence since the deadlock began. Samak imposed a state of emergency in Bangkok following the violence, but the military has not removed the demonstrators.
Still, the possibility of a military intervention hangs over Thailand, which has experienced 18 military coups since the country became a constitutional monarchy in 1932.
Analysts say new elections might ease the pressure on the government but won't placate the alliance because Samak's party is likely to return to power, thanks to the strong support it has in rural areas.
The alliance claims to be an apolitical group and is made up largely of royalists, wealthy and middle-class urban residents, and union activists.
"What they want is to eradicate Thaksin and his allies once and for all," said Panithan Wattanayagorn, a political analyst.
The alliance argues that Western-style democracy doesn't work for Thailand. It says the ballot box gives too much weight to the impoverished rural majority who are susceptible to vote buying that breeds corruption. It wants Parliament to be revamped so most lawmakers are appointed rather than elected.
The government's failure to resolve the deadlock has also raised fears of an economic downturn.
Since the beginning of the year, the Stock Exchange of Thailand index has fallen 24 percent. In the second quarter, the country's economic growth slowed for the first time in more than a year. The central bank expects growth to ease further in the second half because of the political crisis.
"The country is at risk of becoming ungovernable," the Credit Suisse Group said in a report.