His remarks come amid protests over the notification issued by his ministry on the sale of cattle for slaughter at open markets across the country.
"We drafted the rules after the Supreme Court directive. Following this, the notification was put in the public domain for a period of one month.
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The row over beef eating and cattle trade has led to protests in several states, including Tamil Nadu, Kerala and Karnataka.
Vardhan said suggestions "are coming in and if anybody has any reservations, they can send it to the ministry and these suggestions will be looked at objectively.
"Now the matter is again in the Supreme Court," he said.
The Madras High Court had on May 30 stayed for four weeks the enforcement of the contentious notification.
The order had come on a petition challenging the bar as inimical to personal liberty, people's rights to livelihood and an encroachment into matters that are within the domain of the states.