Calling his opponents, the People's Alliance for Democracy (PAD), a "freak cult", he said they were seeking anarchy and he would remain to "protect democracy".
Noting several times that the world was watching Thailand, he said the political crisis was a "shameful" embarrassment to the country.
"These people want the government to quit, but how could I do that if the entire world is watching?" he said.
If his opponents wanted him out, they should use the courts and not take to the streets, the prime minister added.
Al Jazeera's Selina Downes, who was with protesters at Government House where they remained encamped on Thursday, said it was not the speech that they wanted to hear.
Samak's opponents, who had expected him to announce his resignation in the radio address, 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 such talk was rubbish, dismissing any fracture within the alliance.
Sondhi said Samak was a "master of deception and he lies about everything".
Samak also thanked union members for not going on strike on Wednesday.
They PAD and sympathetic unions had called for a general strike to disrupt transportation services and cut off water and power supply 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.
The PAD had appeared to change tack on Wednesday and 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 on Thursday it reversed its position after the prime minister's 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 own 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 respected 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 intensifying street protests against his seven-month old administration.
But thousands of anti-government protesters have publicly 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 committed 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.