Samak's comments came a day after Jakrapob Penkair, a minister attached to the prime minister's office, resigned after being accused of insulting Thailand's king, who is widely revered throughout the country.
Protesters led by the People's Alliance Democracy (PAD) had been demanding the minister's resignation in addition to their calls for the overthrow of the government.
"I am resigning because there is too much pressure on the prime minister and the government," he told a press conference in Bangkok. "I had no intention of insulting the monarchy."
The demonstrators accuse Samak of trying to illegally change the military-backed constitution to cling to power and allow Thaksin Shinawatra, a former prime minister, to evade corruption charges against him.
The protests are similar to demonstrations in October 2006 that led to the overthrow of the government in a military coup.
The head of Thailand's army has sought to allay fears of the military stepping in.
General Boonsrang Niumpradit, who has a largely ceremonial role, said the army would only enforce law and order if the current protests escalate.
Samak, who is widely viewed as a proxy of Thaksin, has accused the PAD - an anti-Thaksin party which has vowed to step up the protests - of damaging the country.
Since the end of the absolute monarchy in 1932, Thailand has seen at least 18 coups or coup attempts.