Thai protesters defy PM's warning of a crackdown
Riot police were deployed, but the authorities did not carry out the PM's threats, saying force would not be used as long as the protest was peaceful.
Opposition activists accuse Mr Samak of changing the constitution to protect his predecessor, Thaksin Shinawatra.
Reports say the instability coincides with rumours of an imminent coup.
The demonstration was led by the People's Alliance for Democracy, the group who led mass protests in 2006 that led to the military coup that ousted Mr Thaksin.
On Saturday, some protesters wore helmets and masks, apparently to protect themselves in case tear gas was used.
There has been heightened political tension and demonstrations in recent weeks over the government's plans to revise the military-drafted constitution.
The opposition says Mr Samak is a close ally of Mr Thaksin, who they believe has a hidden, anti-monarchy agenda.
It says Mr Samak is trying to change the military-backed constitution to hold on to power and to prevent Mr Thaksin from facing corruption-related charges.