The chief ministers of the states described the ban as an infringement on state powers and asserted that they would challenge it in courts of law.
Abattoirs across India on March 31 called off a strike after four days when the most populous state of Uttar Pradesh, ruled by Modi's party, gave assurances that it would renew the licences of slaughterhouses and protect them against the attacks from cow vigilante groups.
The rules, which took effect Friday, require that cattle traders pledge that any cows or buffalos sold are not intended for slaughter.More news: Penguins outshot and outplayed, but outlast Predators 5-3 in Game 1
"In the garb of the order that prohibits the trading of cattle at organised markets, the government has tried to impose a ban on the meat industry", Abdul Faheem Qureshi, head of the Muslim All India Jamiatul Quresh Action Committee, told news agency Reuters.
The government last week prohibited the sale and purchase of cows - an animal considered sacred for Hindus - for slaughter across India. The prime minister, Narendra Modi, ran for office in 2014 on a platform of banning their slaughter nationally.
Others say the ban will hurt farmers who will be forced to continue feeding aged animals, and that millions of unproductive cattle will be turned out on the streets. The industry experts pointed to last year's data, saying that India exported 1.33 million tons of buffalo meat during financial year 2016-17, which amounted to a staggering $3.9 billion.More news: Texas' Scottie Scheffler, UNLV team lead NCAA golf
Chief Minister Mamata Banerjee said the state would not accept the imposition of such restrictions on its commercial authority. "You can not suddenly get up and compare them to ones in advanced countries like the USA or United Kingdom", he said. But the movement to ban their slaughter is usually traced to the late 19th century, when Hindu activists began building a modern political platform out of the extraordinary array of beliefs and practices that form the ancient religion.
Though restrictions on beef are in place across much of India, states such as West Bengal, Kerala and in the north-east of the country consider the meat a staple, even among Hindus. Cases of slaughtering cows have triggered communal violence.
Mr Modi's critics say the new order is aimed at appeasing India's Hindu community.More news: Texas Gov. Greg Abbott mulling special legislative session