Jaswant's supporters and well wishers started the yagya at the Muketeshwar Mahadev Temple premise for his long life, Pooran Singh Bhati, chairman of Jaisalmer Development Bank, said.
Some other fans of Jaswant held a similar yagya at Baisahki village on Saturday, Bhati said.
Jaisalmer Rotary Club President Mayan Bhatiya and a young BJP leader were also separately holding prayers for Jaswant's recovery from coma.
The 76-year-old former defence minister was admitted to the hospital at around 11 pm on August 7 after he fell down at his residence.
Singh, who had also served as External Affairs, Defence and Finance Minister in Vajpayee government, was expelled from the BJP early this year after he decided to contest the Lok Sabha polls from Barmer in Rajasthan as an Independent after being denied a ticket.
Modi, Manmohan Singh visit ailing Jaswant Singh
Former BJP leader Jaswant Singh on life support
Former BJP leader Jaswant Singh in coma