The potential protests by anti-government groups have raised enough concern the government has invoked provisions of an internal security law in three districts in Bangkok, the Bangkok Post reported.
Police estimated the number of protesters at 4,000 but said the number could go as high 70,000.
Critics of the amnesty bill claim its primary purpose is to enable fugitive former Prime Minister Thaksin Shinawatra to return home.
The bill is scheduled to be debated Tuesday and the People's Army against the Thaksin Regime has threatened to hold a rally Sunday that would continue until the day of the debate.
The United Front for Democracy Against Dictatorship backs the bill but said it would avoid confrontations with protesters out of concern any disturbances would be used as a pretext to oust the government.