The Left party described the Centre's notification as an "assault" on fundamental rights of citizens and alleged encroachment of powers of states.
"The issue will be raised in the forthcoming session of the Parliament. The government will have to withdraw this notification," CPI national secretary D Raja said.
Raja rued the government took such a "big" decision without consulting Parliament in confidence.
The Centre on May 26 banned the sale and purchase of cattle from animal markets for slaughter, a move that is expected to hit exports and trade of meat and leather.
It also prohibited practices that are cruel to animals including painting of horns and putting ornaments or decorative materials on them.
The environment ministry has notified the stringent 'Prevention of Cruelty to Animals (Regulation of Livestock Markets) Rules, 2017' under the Prevention of Cruelty to Animals Act.