"Broad consensus should be arrived at among secular democratic forces, opposition parties and also state governments on the bill for which the government should take initiative," CPI Central Secretariat said in a statement.
It said that the legislation should be brought in this session of Parliament, maintaining there was a necessity for such a bill as the country has witnessed many communal attacks in the last six decades.
"It is no surprise that Sangh Parivar and its political wing oppose any bill intended against communal violence. The recent shameful communal violence in Muzaffarnagar in Uttar Pradesh reminds the urgency of the bill to be tabled in the Parliament for a discussion and adoption," the party said.