The interim order of the Madurai bench of the Madras High Court came following protests in some states including Tamil Nadu and Kerala against the measure.
Under relentless opposition attack, the government, meanwhile, said it was examining "issues" raised by some state governments and trade organisations.
A defiant West Bengal Chief Minister Mamata Banerjee had yesterday called the new rules "undemocratic and unconstitutional" and declared it would be challenged legally.
Kerala Chief Minister Pinarayi Vijayan had termed the ban "anti-federal, anti-democratic and anti-secular", and shot off letters to his counterparts in other states asking them to "stand together" and oppose it. He also urged Prime Minister Narendra Modi to withdraw the new regulations.
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Petitioners Selvagomathy and Asik Ilahi Bhava also contended that the provisions breached the "cardinal principle of federalism" as it amounted to legislation in areas earmarked for state legislatures.
Referring to the contention of the petitioners that the notification related to food and hence ought to have been discussed in Parliament, the judges asked the Centre to respond to the point also in its counter-affidavit.
Meanwhile, Union minister M Venkaiah Naidu said in New Delhi the government was examining the issues raised by states and trade organisations against the ban.
The ban, he said, was notified against the backdrop of some observations made by the Supreme Court and a parliamentary committee on preventing cruelty to animals.
The Environment Ministry, which had notified the rules last week, has received 13 representations regarding those.
Officials in the Environment Ministry said they are studying them.
Meanwhile, Mamata Banerjee, who had said yesterday she does not "accept" the ban, today asked the state police not to comply with the Centre's notification.
"What someone will eat is his or her personal choice. No one has the right to dictate. Don't follow that order. The state has not given any such order. The administration should ensure that there is no confusion. Until the state government gives an order (in this regard), don't follow it (the Centre's ban order)," she told an administrative review meeting in Barrackpore.
Several places in Kerala and Tamil Nadu have witnessed protests during the past few days against the ban, with those opposed to it hosting 'beef fests' and saying the Centre's decision interfered with the food habits of people.
The petitioners said the provisions were notified on May 23 last when courts were on vacation. Such rules should have been discussed in parliament and approved by it. Rules prohibiting sale and purchase of animals violated the right to freedom of religion guaranteed under Constitution, they submitted.
The farmers and other traders involved in the sale of cattle, and slaughter houses and their employees would be deprived of their right to livelihood, the petitions said.
The petitioners also contended that the matter came under the legislative domain of state legislatures and "breached the cardinal principle of federalism".
The cattle ban controversy came in the midst of a festering row over cow slaughter and consumption of beef.
Some opposition leaders have claimed the new rules to regulate the livestock market was part of the RSS-BJP "agenda" to impose a nation-wide ban on beef consumption.
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