The Centre said they are ready for amendments in the notification on cattle sale and would be re-notified after considering suggestions.
The Madras High Court had already stayed for four weeks the Centre's notification banning sale and purchase of cattle for slaughter.
In its interim order, a Madurai bench comprising Justices M V Muralidharan and C V Karthikeyan directed the central government to file its counter in four weeks.
The controversial central notification banning sale and purchase of cattle at animal markets for slaughter was challenged in the Supreme Court on June 7.
The matter was mentioned before a vacation bench of Justices Ashok Bhushan and Deepak Gupta for an early hearing.
The petitioner had contended that the provisions in the notification were unconstitutional as they violated the fundamental rights including freedom of conscience and religion and right to livelihood.
The plea had claimed that the government notification issued last month was "against the freedom of religious practice to sacrifice the animals" and imposing a ban on slaughter of animals for food violates the right to food, privacy and personal liberty guaranteed to a citizen under the Constitution.