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 a referendum.
"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," added deputy government spokesman Nattawut Sai-gua.
The announcement was met with scepticism from the anti-government protesters camped in the compound of Mr 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 People's Alliance for Democracy is talking about," said former Senate vice-president Pichet Pattanachote, who has joined the alliance.
"This protest is about making sure the government corrects its mistakes."
Just hours before the decision, a defiant Mr Samak went on national radio and vowed that he would not step down.
His combative speech intensified the deadlock with the People's Alliance for Democracy, thousands of whose supporters have taken over the sprawling lawns of Mr Samak's office compound since storming through the gates on August 26.
Describing the alliance as an anti-democratic group and their actions as a shameful embarrassment for the country, Mr Samak said that he will not bow to its demands.
"I will not abandon the ship, and I will take responsibility for the crew on board," mr Samak said. "I am not resigning. I have to protect the democracy of this country."
The alliance has already helped force one prime minister from power, holding demonstrations in 2006 that paved the way for the bloodless military coup that removed Thaksin Shinawatra. The alliance accuses Mr Samak of being a proxy for Mr Thaksin.