West Bengal in eastern India and Kerala in the south said they would not follow the "arbitrary" order which bans the sale of cattle at livestock markets.
The federal government said the order was aimed at "preventing uncontrolled and unregulated animal trade".
But critics say the move is aimed at protecting cows, considered holy by India's majority Hindu population.
West Bengal and Kerala are among several Indian states where beef is part of local cuisine.
Correspondents say the order will hurt farmers, and industries like food processing and leather.
Many states have actively started enforcing bans on cow slaughter after the Hindu nationalist Bharatiya Janata Party formed India's federal government in 2014.
The western state of Gujarat passed a law in March making the slaughter of cows punishable with life imprisonment. In addition to government bans, several vigilante groups who portray themselves as protectors of cows have also been active in several states.
Such groups have even killed Muslim men over suspicion of cow slaughter. Prime Minister Narendra Modi last year criticised the vigilantes, saying such people made him "angry".
However, this has not stopped attacks against cattle traders.
Mr Modi's critics say the new order is aimed at appeasing India's Hindu community.
West Bengal Chief Minister Mamata Banerjee said the centre was "encroaching upon state matters" with such orders.
"Prevention, protection and improvement of stock and prevention of animal diseases come under the state list. So do markets and fairs and also trade and commerce," she said.
Kerala Chief Minister Pinarayi Vijayan has written to all non-BJP ruled states to unite against the order.
He said it violated India's federal constitution and also violated "the basic right of a person to freedom of choice regarding his food".
The union territory of Pondicherry has also decided to formally oppose the ban.
The southern states of Karnataka and Telengana as well as Meghalaya in the north-east have also protested the order.
Several Indian states have opposed the federal government's decision to ban the sale of cattle for slaughter.