Samak Sundaravej yesterday proposed the referendum, but no details were given of what questions it might put forward.
The protestors, who call themselves the People's Alliance for Democracy, are an ad-hoc alliance of royalists, businessmen and academics who are opposed to the prime minister.
They say Mr Samak is a puppet of the deposed former prime minister, Thaksin Shinawatra, who is now in exile in London.
Protestors began an occupation of the grounds of the prime minister's compound 11 days ago, and violent clashes between them and government supporters last Tuesday left one man dead and 45 injured.
Prime minister Samak then declared a state of emergency, but the country's army chief, General Anupong Paojinda, has so far refused to evict the demonstrators.
Late yesterday a gunman on a motorcycle fired shots at a group of about 100 students marching to protest at Mr Samak's home, injuring two of them.
