A division bench of Chief Justice Subhash Reddy and Justice V M Pancholi also issued notices to the state and central governments.
The bench had on last Wednesday issued notices to three respondents on a PIL filed by one Anil Dave seeking a ban on the game on the ground that, among others, the game hurts religious sentiments by showing images of eggs in places of worship of different religious groups.
Both the PILs will now be heard together on October 12.
In the fresh PIL, petitioner Sanjay Chaudhari argued that various countries have responded differently to tackle the problems of public safety, arising out of the game.
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Chaudhari pleaded to HC to issue directions to the central government to either clamp a blanket ban on downloading the game or allow it to be played only in public parks.
The PIL stated that while countries like Iran, Vietnam, and some in the African continent have completely banned the game, in countries like Australia, Japan, the US and Russia police have been asked to take stern action against those violating the law while playing the game.
"In India also, cases of accident have been reported in Mumbai and Vadodara because of playing the game," the PIL said, adding that a museum in Vadodara has even put up a notice prohibiting entry to Pokemon Go players.