The demand stems from the rape of a seven-year-old girl in her school toilet yesterday.
Congress leader Aleixo Reginaldo Lourenco told reporters that fast track courts should be established to try rape cases, so that the accused is punished without delay.
"Government should provide all infrastructure on an urgent basis to set up such courts," he said.
Lourenco demanded that all schools in Goa should be equipped with CCTV cameras and security around them should be increased.
"We demand that government should immediately initiate steps to provide security to girl children. Installation of cameras in schools should be made mandatory," he said.