Somsak said on Thursday the process for drafting the referendum will start immediately.
Hours earlier on live radio, Samak said he will not resign nor see any reason to dissolve parliament.
However, Abhisit Vejjajiva, the Democrat party leader, told Al Jazeera it was probably "unconstitutional" to hold a referendum on a person or a group of people.
"If the PM really would like the verdict of the country, why not dissolve the house?" he said.
"We're not disputing that the house is democratically elected, but subsequent actions by this government is judged to have been wrong ... violating the constitution by the constitutional court, as well as a series of scandals.
"In any civilised democracy, the government would have shown some kind of responsibility or accountability by now."
The cabinet move to break the political impasse came a day after Tej Bunnag, the foreign minister, resigned.
Samak is facing repeated calls to resign from anti-government protesters led by the People's Alliance for Democracy (PAD) who have been camped out on his office lawn since last week.
He has repeatedly refused to resign, vowing not to bow to the demands of street protesters he described as a "freak cult" seeking anarchy.
He insisted that he will "stay in order to preserve democracy and to protect the monarchy".
If his opponents wanted him out, they should use the courts and not take to the streets, he said.
The referendum, if it proceeds, will be only the second ever in the kingdom. The first was in 2007, passing a new military-backed constitution formed after a coup a few months earlier.
In Bangkok, Al Jazeera's Selina Downes who was with protesters at Government House, said it was not the speech that they wanted to hear.
Samak's opponents, who had expected him to announce his resignation, reacted angrily to his speech and shouted for him to "get out", she said.
The digging in of the prime minister's heels has thrown up suggestions that there might now be a split within the PAD on what to do next, but Sondhi Limthongkul, who leads the group, said dismissed the possibility of any fracture within the alliance.
Sondhi said Samak was a "master of deception and he lies about everything".
The PAD and sympathetic unions had earlier called for a general strike to disrupt transport services and cut off water and power supplies to government offices, but were bitterly disappointed when it failed to materialised.
Samak's announcement on Thursday indicated that the standoff with his opponents was unlikely to be resolved soon.
On Wednesday, the PAD had appeared to change tack when it said only Samak, instead of the whole government, needed to resign, a move that may have undermined support from Samak's coalition partners and put more pressure on him to go.
But it reversed its position a day later following the prime minister's radio address, saying the whole government was guilty of vote-buying in December's elections and so the entire government must go.
Pressure mounted on Samak on Wednesday when his foreign minister resigned, a move widely viewed as a sign that Samak was losing support from his government.
Tej Bunnag was formerly a royal adviser and he had been seen as a link for Samak to the royal palace, so his resignation was a big blow to the prime minister.
|Tej was seen as Samak's link to the royal palace [AFP]
Some analysts said Tej was jumping from Samak's sinking political ship.
Samak said Tej, a diplomat who was appointed to his post on July 27 to help ease political tensions, had been "pressured by many sides" and that his wife was not well.
His resignation came a day after the prime minister invoked emergency rule in the capital, Bangkok, to quell street protests against his seven-month-old administration.
But thousands of anti-government protesters have humiliated Samak by defying the emergency decree and remaining at his office compound, after the army declined to use force to remove them.
Samak also faces a legal challenge after the country's election commission recommended that his People's Power party (PPP) be disbanded for alleged electoral fraud during December's elections.
The commission on Tuesday forwarded its findings to the attorney-general's office to decide whether to submit the case to the constitutional court for a final ruling.
Samak and other party leaders would be banned from politics for five years if the ruling is upheld, although other members could form a new party and retain power by winning new elections.
Tuesday's move was reminiscent of the court dissolving of Thaksin's Thai Rak Thai party last year. The party later regrouped under the PPP flag.