The plea for urgent hearing was mentioned before the vacation bench of Justices Adarsh Kumar Goel and L Nageswara Rao, which agreed to list the matter during the week.
Senior advocate Anand Grover appearing for the petitioner animal activist Gauri Maulekhi said the Centre does not have power to issue such notification.
He said that people were being hired for mass killing of these three animals which have been declared as vermins.
The second notification of the ministry dated February 3, 2016, declared wild boar as vermin in some districts of Uttarakhand for a one-year period.
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The third notification, issued on May 24, 2016, declared rhesus macaque (monkey) to be vermin in some districts of Himachal Pradesh.
"The impugned notifications have been passed in absolute disregard of the human-wildlife conflict plaguing the country and without any scientific survey backing them," the plea said.
"The State is no longer responsible for safeguarding the life and well-being of such animals. The indiscriminate killing of these animals will have a detrimental effect on the food chain and in turn lead to an ecological imbalance," the plea said.
It said the provisions of the Act "authorises the government to permit mindless slaughter of protected wildlife without any inquiry or investigation into the need for declaring protected species of wildlife as vermin for purpose of slaughter."