"I am not afraid but I am concerned about chaos in the nation," Samak said in his national address.
As politicians prepared to hold their emergency meeting on Sunday, protesters remained camped on the grounds of Samak’s office.
Police have used tear gas on occasion, but have chosen to take a non-confrontational approach at other times, leaving the protest to take on a carnival-like atmosphere.
Al Jazeera's Selina Downes, reporting from Bangkok, said that a pro-government lobby had started to gather near the demonstrators outside Government House office complex.
"There are about 1,000 government supporters. They call PAD a political mafia and argue that this government was elected. They say they are trying to uphold the principles of democracy, so the prime minister has been thrown something of a lifeline."
On Sunday there was no visible police presence at the prime minister's compound.
"We cannot let the seizure of Government House continue indefinitely without taking action," Samak said.
|Samak addressed the nation on state-run television [Reuters]
Samak concedes that his government and the courts have failed to evict protesters and now needs the support of the parliament.
"Since the government cannot resolve the problem - even the courts cannot resolve the problem - the joint session of parliament is the best choice for finding a solution," he said.
On Saturday, Samak met King Bhumibol Adulyadej, the head of state. Reporters had expected him to make a statement on his return to Bangkok, the capital, but he avoided them at a military airfield.
The unrest reached a peak on Friday when Bangkok police fired tear gas and rubber bullets to repel an assault on their headquarters by about 2,000 protesters.
Thousands of foreign tourists are still stranded on the resort of Phuket after the island's airport closed.
Samak said: "The Phuket security must be reviewed. They have been trained to handle terrorists but what happens? How have they allowed these people to encroach on the runway?"
"They have destroyed Thailand's image as the most attractive tourist destination."
The six parties in the government coalition expressed support for Samak on Saturday.
Speculation is growing that Samak will call a snap election. His People Power Party has strong support in the rural areas.
Parliament is to debate the government budget for the coming year on Wednesday. It is expected to be approved and would give sitting ministers funds to spend in ways that would support their election prospects.
Thai shares have fallen 23 per cent since the street protests began in May amid fears of major unrest or policy paralysis at a time of stuttering economic growth and high inflation.