The FIR was registered at Chauhatan police station based on a complaint filed by a local resident, Pathai Khan, a police officer said.
"Bapu, I am here today not as a Prime Minister, but as a Hindu," said Sunak, opening his address at the gathering.
The annual Amarnath yatra to the 3,880-metre high cave shrine in the south Kashmir Himalayas will commence on June 28 and culminate, as per the tradition, on the day of Raskha Bandhan festival on August 22, officials said.
Desai, along with three of her colleagues took darshan of the 'shivlinga' in the 'garbha gruha' around 6 am and left after nearly 15 minutes.
BJP leader Vinay Katiyar said like a Shiva temple, water drips from the ceiling in the Taj Mahal.
These people don't know that time has changed and they should not treat people as fools, Modi said.