"Jallikattu, a traditional sport which reflects bravery, is an integral part of social, cultural and religious sentiments of Tamils. The Tamil Nadu government is making all- out efforts to resume it," Reddy told the state Assembly.
He said the issue of jallikattu's conduct "has been under judicial scrutiny since 2006".
The minister said the government, in a bid to resume the sport banned by the Supreme Court in May 2014, also knocked on the Centre's door.
Accordingly, the Environment and Forest Ministry had issued a notification on January 7, 2016 to conduct the sport but the Supreme Court issued an interim stay on January 12, he said.
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The minister recalled that Jayalalithaa had immediately urged Modi to promulgate an ordinance to enable conduct of jallikattu.
In March, the state government filed a common counter affidavit in the apex court for the conduct of the sport, Reddy said, adding Jayalalithaa took up the matter with Modi again in June.
Reddy said the governor, in his address to the Assembly in June, had also mentioned that steps would be taken to "lift the ban" against holding the sport.