The incident occurred at the Swamy Venkateswara Temple in the Srikakulam district of Andhra Pradesh state where hundreds of devotees had gathered to mark one of Hinduism's sacred days, Ekadashi.
On this day, the devotees fast and offer prayers to Lord Vishnu, a key Hindu deity.
An initial investigation suggests that an iron grille meant to maintain the queue of worshippers at the temple broke, leading to the uncontrolled crowd surge, senior police officer KV Maheswra Reddy told the Associated Press.
Senior local government official Swapnil Dinkar Pundkar said more casualties were feared.
"Initially, we had reports of seven deaths but two more people have succumbed to their injuries while the condition of two others is critical," he said.
Of the dead, eight were women and one was a child, Pundkar said, adding that at least 16 devotees injured in the crowd surge are being treated at a local hospital while 20 others are in a state of shock and put under observation at a different hospital.
Video on local media showed people rushing to help those who fainted in the crowd surge and were gasping for breath.
Some were seen rubbing the hands of those who fell on the ground.
Prime Minister Narendra Modi and Andhra Pradesh's highest-elected official N Chandrababu Naidu expressed grief and offered their condolences to the families of the bereaved.
Crowd surges at religious gatherings are not uncommon in India, where massive groups often congregate at temples or pilgrimage sites, sometimes overwhelming local infrastructure and security measures.
In July, a crowd surge at a popular Hindu temple in northern India left at least six people dead and dozens injured.
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