The senders claimed to be members of terrorist organisation Jaish-e-Mohammad.
Sat Kaival is a religious sect with a big following in the region and also among NRIs.
The letters were written in Hindi and Gujarati, local police said. The writers claimed to have conducted a recce of the temple and said they will blow it up and kill Avichaldasji to take revenge for Babri Masjid demolition and Godhra riots.
"Police can't do anything and even (Prime Minister Narendra) Modi can't save you... You know what happened to Pravin Togadia's relative in Surat," it said.
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Avichaldasji, who is also the national secretary of Akhil Bhartiya Sant Samaj, recently attended Simhasth Kumbh Mela in Ujjain where he delivered discourses against cow slaughter, a member of the temple management said.
Superintendent of police Saurabh Singh said police would provide security to the temple and the priest.
Manager of the temple trust Hitesh Patel filed a complaint regarding the threat letters at Khambhoji police station.